When the Constitutional Convention adjourned on September 17, 1787 the document the delegates left with eventually became the U.S. Constitution. Eventually being the operative word. Each state still had to ratify the document by a vote of their individual legislatures in order to be bound by it. Debates flared concerning ratification, with the two main camps being the Federalists (generally supporting the document's ratification, believing a stronger centralized government was desirable - especially after the weakness of the Articles of Confederation which governed the states before the Constitution's ratification) and Anti-Federalists (generally opposing ratification, many suggesting the Constitutional Convention was an illegal body or that the document gave too much power to a central government). Virginia and New York, the two most populous and wealthy states, hesitated in the ratification of the Constitution, which produced a fertile ground for the debate between the parties to unfold.

The most well known forum for the debates were referred to as the "Federalist Papers," and consisted mostly of the Federalist arguments and counter augments in support of the document. The majority of these "Papers" were written by founding fathers you are familiar with such as Madison, Hamilton, and John Jay writing under pseudonyms. I suggest reading the Wikipedia article on the Federalist Papers if not reading the documents themselves.

The Federalist's eventually won out, but not before promising to quickly amend the Constitution to add what would become the Bill of Rights (actually 12 amendments were suggested, 10 ratified). Anti-Federalists held out for the promise of these amendments because of fear that the document did not protect individual liberty sufficiently (Federalist's generally believed the Constitution as written was sufficiently constricting on the Federal government, but agreed to vote for or at least not oppose the suggested amendments).

With the promise of amendment additions immediately after ratification of the Constitution, some opposed to ratification were sufficiently convinced that the newly stylized Federal government was constricted enough by the Constitution (with an added Bill of Rights) to protect individual citizens that their votes carried the hesitant states.

On December 15, 1791, Virginia became the 10th of 14 states to ratify the first 10 proposed amendments, securing the necessary two-thirds vote to ratify the Bill of Rights.