Question

Why did the promise of a bill of rights convince many delegates at state ratification conventions to vote in favor of the constitution?

Answer 1

Because Their individual rights and liberties would be protected.
The bill of rights consists of several amendments that guarantee basic liberties for all citizens in united states, such as the right to live, the right of speech, the right to pursue happiness, etc.
In people's perspective, these basic liberties will protect us from a tyrannical government.