Alaska Bypass Modernization Act of 2014

Alaska Bypass Modernization Act of 2014 - Amends provisions of federal law relating to Alaska bypass mail transportation to require the U.S. Postal Service (USPS), in selecting a carrier of nonpriority bypass mail to a point in Alaska, to ensure: (1) a minimum of one scheduled flight per week to each nonpriority bypass mail destination with guaranteed capacity for nonpriority bypass mail, subject to the condition that the weather, lack of available service, or other extraordinary circumstances do not interfere with the fulfillment of such minimum requirement; and (2) that any flight that transports nonpriority bypass mail to a nonpriority bypass mail destination and that is in addition to the minimum flight requirement is necessary to the delivery of nonpriority bypass mail and maximizes the cost efficiency to USPS. Revises provisions relating to the tender of nonpriority mainline mail to bush carriers and between qualified passenger and nonmail freight carriers from an acceptance point in Alaska.

Modifies requirements and definitions relating to contracts for foreign and interstate air transportation. Authorizes USPS to contract for the transportation of mail by aircraft between any of the points in foreign air transportation only with certificated air carriers.

Treats Alaska bypass mail service as a separate competitive product for all purposes and prohibits the transfer of such service to the market-dominant category of mail.

Revises the schedule of rates and fees for matter sent by Alaska bypass mail service to cover at least 30% of costs attributable to such service in FY2015, with increasing percentages until FY2020, in which year 50% of such costs will be covered. Limits in FY2014-FY2020 any increase in the rate for any type of Alaska bypass mail service by more than the maximum permitted rate increase for market-dominant products plus an additional 1%.  Requires the Postal Regulatory Commission (PRC) to determine, at least once each fiscal year, if USPS is in compliance with such rate schedule. Prohibits PRC from ordering USPS to discontinue Alaska bypass mail service.