A woman from Louisiana who has allegedly been following the actress and singer Betty Buckley wherever she goes will be arrested for trespassing if she appears on Saturday at the Bay Street Theater’s summer benefit, where Ms. Buckley will be performing.The woman, whose name was not released because she has not been charged with a crime, showed up at the theater’s box office at curtain time Monday for Ms. Buckley’s “Music Mondays” performance. Tracy Mitchell, Bay Street’s executive director, called Sag Harbor Village police, but the woman was gone when officers arrived.She returned, however, about an hour and a half later, lingering just outside the theater. Police returned too, and found her nearby on Long Wharf, where they warned her to stay away or face arrest. The stay-away zone includes Bay Street’s outdoor space, where there are tables and chairs for theater patrons.Ms. Mitchell was seen on Monday at police headquarters, picking up copies of the paperwork ordering the woman to stay off the property. She spoke briefly before leaving the station, saying the woman follows Ms. Buckley from performance to performance around the country. Bay Street’s staff is familiar with her routine, Ms. Mitchell said, but at venues where Ms. Buckley performs for the first time, the staff can be fooled. She insinuates herself into theaters by pretending to be a close friend of Ms. Buckley’s, said Ms. Mitchell, and even tries to get onto the stage.