Bay Street Theater in Sag Harbor has announced that the musical “Grey Gardens” will be part of its 2015 Mainstage season, with a run from July 28 through Aug. 30. Based on the 1975 documentary film by Albert and David Maysles about Big Edie and Little Edie Bouvier Beale, the show has a book by Doug Wright, music by Scott Frankel, and lyrics by Michael Korrie. Casting and the creative team will be announced at a later date, as will next summer’s other productions.