While there were delegates at several conventions who supported an "amendments before" approach to ratification, it soon shifted to an "amendments after" for the sake of trying to hold the Union together. Ultimately, only North Carolina and Rhode Island waited for amendments from Congress before ratifying.
Four days prior to the conclusion of the Virginia Convention, on June 21, 1788, New Hampshire ratified the Constitution. What makes that date special is that when New Hampshire ratified, with its 12 proposed amendments, the required number of state ratifications, according to Article VII of the Constitution, had been met to establish the Constitution. [Article VII - "The ratification of the conventions of nine states, shall be sufficient for the establishment of this Constitution between the states so ratifying the same."} The Constitution would become operational. A new union (comprised of those states that had ratified) was created and the new frame of government would be established.
The New York ratification convention met on June 17, 1788, while the Virginia Convention was still debating ratification. As with Virginia, a majority of its 67 delegates were anti-Federalists. (The New York Convention would last over month - from June 17 until July 26). On the opening day, the anti-Federalists, led by Governor Clinton, clamored for a Bill of Rights and fought to preserve the autonomy of the state against what it believed were actual and potential federal encroachments. Hamilton (the only NY delegate to the Philadelphia Convention to sign the Constitution) and the Federalists, on the other hand, contended that a stronger central government would provide a solid base from which New York could grow and prosper. While the debates were contentious, the Federalists were ultimately successful and on July 26, the Constitution was ratified by a very slim margin, 30-27, but with 25 Bill of Rights and 31 proposed amendments. The Convention also voted to call for a second federal convention. [New York's Ratification is provided in the Appendix at the end of this article. Take note of its Bill of Rights - it includes a "Resumption Clause"].
On September 13, 1788, the Articles of Confederation Congress certified that the new Constitution had been ratified by more than enough states for the new system to be implemented and directed the new government to meet in New York City on the first Wednesday in March the following year. On March 4, 1789, the new frame of government came into force with eleven of the thirteen states participating - and without a Bill of Rights.
Opposition to the new Constitution among leading Virginians lingered. It would continue to be a thorn in James Madison's ass... the man who deceived the states into sending delegates to Philadelphia believing they were tasked with proposing amendments to the Articles of Confederation (when all along, he wanted them to take up the issue of an all-new scheme of government - his scheme, the "Virginia Plan"), the man who thought his scheme had finally been realized, and the man who supposedly held that "not a letter of the Constitution" should be altered.
After Virginia's ratification and New York's ratification, the future of the Constitution, as ratified, was not certain. New York wanted to call another federal convention (to amend the new Constitution? To get rid of the new Constitution?) and several powerful Virginians, with Patrick Henry taking the lead, seemed likely to move for the same.
As fate would have it, Madison set his sights on the US Senate. But there was one problem for him - the Constitution (pre-17th Amendment) empowered the state legislatures to elect senators, but the VA state legislature (VA General Assembly) was comprised of many enemies he had made in his efforts to deceive the states at the Philadelphia Convention, to write the Constitution, and to secure its ratification, including the great Patrick Henry. And Henry and his fellow anti-Federalists got the chance to get even: in its selection of Senators, the legislature chose Richard Henry Lee and William Grayson.
Both Richard Henry Lee and William Grayson agreed with Patrick Henry that the Constitution should have been amended to include a Bill of Rights (at the least) before it was ratified. Both, it seems, would favor a second convention.
Madison, at this point, was warming somewhat to the notion of amendments, but it's not sure if he was warming because he agreed that a Bill of Rights is essential to limit powers of government or if he was just nervous that the issue might be the one to sink his Constitution. One thing is for certain though, he would have rather the Constitution be amended by the first option in Article V (amendments proposed by Congress and then sent to the states for adoption) than by a second convention (the second option in Article V; a convention of states). Kevin Gutzman addressed this in his book:
For one thing, some states would oppose a convention so strongly that they would reflexively oppose any amendment it might propose. For another, it would be easier to have Congress propose amendments than to follow the process in Article V of the Constitution for convening another meeting like the one at Philadelphia. Finally, another convention would include members with extreme views on both ends of the political spectrum, enflame the public mind, and produce nothing conductive to the general good. He had seen how the first convention had worked, and he did not want to hazard a second - which, too, would undermine the impression of the American republic's stability left in European capitals by the success of the recent ratification campaign. [James Madison and the Making of America, pg. 241]
Defeated in his bid for the US Senate, Madison decided to stand for the House of Representatives. But again, he would be at the mercy of his nemesis, Patrick Henry. Henry wielded power in the General Assembly, and that power included the ability to draw congressional districts. To spite Madison, he helped draw a map that put Montpelier (Madison's home) in the same district as James Monroe's house. In the Richmond Convention, Monroe had aligned himself with Henry, Mason, and Grayson and had voted "nay" on the vote for ratification. "Because Monroe had been an authentic hero in the revolution - suffering a significant wound in Washington's great victory at Trenton - and had established a respectable legislative record in both Virginia and in the Congress of the Confederation, his opposition would be formidable." [Ibid, pg. 241]
Madison campaigned against Monroe, and due to the contentious issue of the Constitution lacking a Bill of Rights, Madison softened on the issue of adding amendments. Perhaps all the letters that Jefferson sent him at this time emphasizing the need for a Bill of Rights had something to do with it. "If pursued with a proper moderation and in a proper mode [meaning that the First Congress would propose amendments for the states' approval, per Article V], they would serve the double purpose of satisfying the minds of well-meaning opponents and of providing additional guards in favor of liberty." [Ibid, pg. 242]. Taking Madison at his word and believing him to be a man of his word, voters selected him over Monroe for the US House of Representatives.

On March 4, 1789, the first US Congress was seated, in New York City's Federal Hall. The first thing to do was to organize itself. On April 1, the House of Representatives elected its officers, and the Senate did the same on April 6. Also on the 6th, the House and Senate met in joint session and counted the Electoral College ballots for the selection of president. George Washington was certified as president (having been unanimously selected) and John Adams as vice president.
On April 30, 1789, George Washington was inaugurated as the nation's first president, also at Federal Hall, delivering the Inaugural Address that James Madison had written for him. In that message, Washington addressed the subject of amending the Constitution. He urged the legislators:
"Whilst you carefully avoid every alteration which might endanger the benefits of an united and effective government, or which ought to await the future lessons of experience; a reverence for the characteristic rights of freemen, and a regard for public harmony, will sufficiently influence your deliberations on the question, how far the former can be impregnably fortified or the latter be safely and advantageously promoted....."
Madison knew that as long as the concerns of the anti-Federalists regarding the Constitution remained unaddressed, the threat of a new convention would remain, and so he would take the initiative to propose amendments (comprising a Bill of Rights) himself. By taking the initiative to propose amendments himself through the Congress, he hoped to preempt a second constitutional convention that might, it was feared, undo the difficult compromises of 1787, and open the entire Constitution to reconsideration, thus risking the dissolution of the new federal government. Writing to Jefferson, he stated, "The friends of the Constitution, some from an approbation of particular amendments, others from a spirit of conciliation, are generally agreed that the System should be revised. But they wish the revisal to be carried no farther than to supply additional guards for liberty." He also felt that amendments guaranteeing personal liberties would "give to the Government its due popularity and stability." Finally, he hoped that the amendments "would acquire by degrees the character of fundamental maxims of free government, and as they become incorporated with the national sentiment, counteract the impulses of interest and passion." [Historians continue to debate the degree to which Madison considered the amendments of the Bill of Rights necessary, and to what degree he considered them politically expedient; in the outline of his address, he wrote, "Bill of Rights-useful-not essential-"]. (see Wikipedia)
On June 8, Madison introduced a series of Constitutional amendments in the House of Representatives for consideration. Among his proposals was one that would have added introductory language stressing natural rights to the Preamble. Another would apply parts of the Bill of Rights to the states as well as the federal government. Several sought to protect individual personal rights by limiting various Constitutional powers of Congress. He urged Congress to keep the revision to the Constitution "a moderate one," limited to protecting individual rights.
Madison was deeply read in the history of government and used a range of sources in composing the amendments. The English Magna Carta inspired the right to petition and to trial by jury, for example, while the English Bill of Rights of 1689 provided an early draft for the right to keep and bear arms and also for the right against cruel and unusual punishment.
The greatest influence on Madison's text, however, was existing state constitutions, and especially Virginia's. Many of his amendments, including his proposed new preamble, were based on the Virginia Declaration of Rights, which were drafted in 1776 by another great nemesis, anti-Federalist George Mason. To reduce future opposition to ratification, Madison also looked for recommendations shared by many states. He did provide one, however, that no state had specifically requested: "No state shall violate the equal rights of conscience, or the freedom of the press, or the trial by jury in criminal cases." He did not include an amendment that every state had asked for, one that would have made tax assessments voluntary instead of contributions. Madison's proposed the following constitutional amendments:
First. That there be prefixed to the Constitution a declaration, that all power is originally vested in, and consequently derived from, the people.
That Government is instituted and ought to be exercised for the benefit of the people; which consists in the enjoyment of life and liberty, with the right of acquiring and using property, and generally of pursuing and obtaining happiness and safety.
That the people have an indubitable, unalienable, and indefeasible right to reform or change their Government, whenever it be found adverse or inadequate to the purposes of its institution.
Secondly. That in article 1st, section 2, clause 3, these words be struck out, to wit: "The number of Representatives shall not exceed one for every thirty thousand, but each State shall have at least one Representative, and until such enumeration shall be made;" and in place thereof be inserted these words, to wit: "After the first actual enumeration, there shall be one Representative for every thirty thousand, until the number amounts to-, after which the proportion shall be so regulated by Congress, that the number shall never be less than-, nor more than-, but each State shall, after the first enumeration, have at least two Representatives; and prior thereto."
Thirdly. That in article 1st, section 6, clause 1, there be added to the end of the first sentence, these words, to wit: "But no law varying the compensation last ascertained shall operate before the next ensuing election of Representatives."
Fourthly. That in article 1st, section 9, between clauses 3 and 4, be inserted these clauses, to wit: The civil rights of none shall be abridged on account of religious belief or worship, nor shall any national religion be established, nor shall the full and equal rights of conscience be in any manner, or on any pretext, infringed.
The people shall not be deprived or abridged of their right to speak, to write, or to publish their sentiments; and the freedom of the press, as one of the great bulwarks of liberty, shall be inviolable.
The people shall not be restrained from peaceably assembling and consulting for their common good; nor from applying to the legislature by petitions, or remonstrances for redress of their grievances.
The right of the people to keep and bear arms shall not be infringed; a well-armed and well-regulated militia being the best security of a free country: but no person religiously scrupulous of bearing arms shall be compelled to render military service in person.
No soldier shall in time of peace be quartered in any house without the consent of the owner; nor at any time, but in a manner warranted by law.
No person shall be subject, except in cases of impeachment, to more than one punishment, or one trial for the same offence; nor shall be compelled to be a witness against himself; nor be deprived of life, liberty, or property, without due process of law; nor be obliged to relinquish his property, where it may be necessary for public use, without a just compensation.