There is something faintly apocalyptic about What Ever Happened to Baby Jane?, the camp classic that brought Bette Davis and Joan Crawford together at the fag end of their movie careers. In Bette & Joan, Anton Burge leans into that sense of twilight, fashioning a two-hander from memoirs and biographies that plays like a backstage Götterdämmerungfor Hollywood’s old guard.

Jeanette Cronin and Lucia Mastrantone in Bette & Joan. Photo © Prudence Upton

Set in adjoining dressing rooms on a B-picture soundstage during the filming of Baby Jane in 1962, Burge’s script cuts back and forth between its two grande dames as they prepare for another day’s shoot. It’s a neat enough device, though the cross-cutting never quite coalesces into anything like dramatic tension. Even as the tone darkens in Act II, when the women get to monologue and eventually share the same space, Bette & Joan remains wedded to the idea of “compare and contrast”.

Under Liesel Badorrek’s direction, however, what might have been a static exercise becomes something livelier: a brittle, often very funny...