The significance of the Bill of Rights in U.S. governance lies in its role as a vital safeguard for individual liberties and rights. The first ten amendments to the Constitution protect essential freedoms such as speech, religion, and the right to a fair trial. By limiting governmental power and ensuring personal freedoms, the Bill of Rights plays a crucial role in maintaining a democratic society. It provides citizens with legal avenues to challenge governmental overreach, enhancing the protection of civil liberties and promoting justice.