Alaska Bypass Fair Competition Act of 2014 - Revises the eligibility requirements for air carriers to be selected by the U.S. Postal Service (USPS) to transport nonpriority bypass mail in the state of Alaska.

Redefines: (1) "existing mainline carrier" as a mainline carrier that, for each of the preceding 36 months, while having met certain certification and qualification standards, engaged in the carriage, on scheduled service within Alaska, of mainline nonpriority bypass mail tendered to it under its designator code (currently, such conditions must have been met as of January 1, 2001); and (2) "new," when referencing a carrier, as a carrier meeting certain requirements that has been providing nonpriority bypass mail service on a city pair route in Alaska for fewer than 36 consecutive months in the immediately preceding period (currently, a carrier is considered new if it began providing such service after January 1, 2001).