Driftnet Modernization and Bycatch Reduction Act This bill addresses certain driftnet fishing. (Driftnet fishing is a method of fishing in which a gillnet composed of a panel or panels of webbing, or a series of such gillnets, is placed in the water and allowed to drift with the currents and winds for the purpose of entangling fish in the webbing.) Currently, the use of large-scale drift gillnets with a total length of 2.5 kilometers or more is prohibited in the United States. The bill expands the definition of large-scale driftnet fishing to prohibit the use of gillnets with a mesh size of 14 inches or greater. This expanded prohibition does not apply within the U.S. exclusive economic zone prior to January 1, 2020. The Department of Commerce must conduct a transition program to facilitate the phase out of large-scale driftnet fishing and to promote the adoption of alternative fishing practices that minimize the incidental catch of living marine resources. Commerce may award grants to program participants.