What portion of the 14th Amendment forced the States to adhere to the Bill of Rights?

The Fourteenth Amendment Due Process and Equal Protection Clauses have both been used, but the Due Process Clause has been used more because many amendments in the Bill of Rights relate directly to protection against abuse from the criminal justice system (due process of law).

Please note that only the First, Fourth and Sixth Amendments have been fully incorporated; the Fifth Amendment is mostly incorporated; The Third and Eighth Amendments are partially incorporated; the Second and Seventh Amendments are currently unincorporated. The Ninth and Tenth Amendments, while considered part of the Bill of Rights, are not amenable to the process.

For more information, see Related Questions, below.