Why did many Americans demand a bill of rights?

Opponents of the new Constitution were worried that it gave too much power to the Federal government, thus potentially undermining Americans' hard-won liberties. The Americans had just successfully defeated Great Britain, which they regarded as a tyrannical power. The last thing anti-Federalists wanted was to see such tyranny reestablished on American soil.
It was in order to assuage the concerns of such critics that the Bill of Rights was passed. The first ten amendments to the Constitution were designed to protect individual states and individuals against the infringement of their inalienable rights by a powerful Federal government. To be sure, the Federal government would still be a good deal stronger than under the Articles of Confederation—it could hardly be weaker—but there would now be specific written safeguards against excessive governmental power.