Alaska Bypass Mail Fairness Act

Alaska Bypass Mail Fairness Act - Amends Federal law pertaining to transportation of mail by air to define nonpriority bypass mail as certain mail prepared by the mailer to bypass postal processing for delivery directly to the recipient under Postal Service prescribed guidelines and conditions, and does not include nonpriority mail dispatched to carriers from a Postal Service facility.

Directs the Postal Service, in selecting carriers of nonpriority bypass mail to any point served by more than one carrier in Alaska, to adhere to an equitable tender policy among qualified carriers (currently, within a qualified group of carriers).

Directs the Postal Service to offer equitable tender of nonpriority bypass mail between an acceptance point and a HUB point at mainline or equivalent rates to certain bush carriers (carriers operating aircraft certificated within certain payload capacity requirements on a city pair route) within Alaska. Requires such bush carriers, to receive such tender, to convert to requirements set forth in the Code of Federal Regulations for domestic, flag, and supplemental operations ("part 121") with respect to at least one aircraft within two years of the enactment of this Act.