Building Bridges and Transforming Resentment and Unfairness to Support and Trust for Municipal Law Enforcement Act of 2014 or the Build TRUST Act of 2014 - Reduces the amount that would otherwise be awarded to a unit of local government under the Edward Byrne Memorial Justice Assistance Grant Program: (1) by 75% for any such unit that, during the previous three fiscal years, funded an amount that on average was greater than 18% of its operating budget using revenue generated from collecting fines and other fees related to violations of traffic laws; and (2) by 95% for any such unit for which, during the previous fiscal year, the percentage of individuals who identify as a race who were employees of the law enforcement agency for that unit and the percentage of individuals who identify as that race who live in the jurisdiction such agency serves differ by greater than 30%.

Reduces by 50% the amount that would otherwise be awarded under such Program to a state that did not reduce a subgrant award to a unit of local government in accordance with this Act in the preceding fiscal year.

Requires the Attorney General to reallocate funds withheld from a state or unit of local government pursuant to this Act in accordance with the Program.

Exempts any local governmental unit which certifies that it serves a population of less than 15,000 or to which the Attorney General has granted a waiver for good cause shown based on specified factors, including that: (1) such unit has taken affirmative action to ensure that adequate practices and procedures are in place to increase public trust and confidence in the impartial and equitable administration of justice, and (2) the minority community is equitably represented in the unit's legislative body and executive departments.