Explain the relationship between the 14th Amendment and the Bill of Rights, as requested in the question.

The most commonly cited relationship between the 14th Amendment and the Bill of Rights is that the 14th Amendment has been used to "incorporate" the Bill of Rights.

The Bill of Rights, as written, applies only to the federal government.  This means that state governments did not originally have to respect the rights given in the first 10 amendments.  Beginning in the early 1900s, the Supreme Court said that the 14th Amendment means that the Bill of Rights applies to state governments as well.  It does this because it says that states cannot deprive people of their "liberty" without due process of the law.  The Court has said that this means states cannot deprive people of their rights under the Bill of Rights.