If there’s a heaven for entertainers, the gateway must be St. Luke’s Theatre. It’s in this church basement that Danny Kaye and Fanny Brice — or, at least, the people playing them — have been holding forth.

Now we also have “The Devil’s Music: The Life and Blues of Bessie Smith,” set in a private, after-hours club in 1937 on the eve of its subject’s untimely death in a car accident.

Describing herself as “one hot and hungry mama,” Bessie (Miche Braden) sings such signature numbers as “I Need a Little Sugar in My Bowl,” “Blame It on the Blues” and “Nobody Knows You When You’re Down and Out” while kibitzing with her backup trio and the audience.

Between generous swigs from a liquor flask — “They say I’m a hard drinker, but honey, that’s the easiest thing I do,” she jokes — she regales us with a bitter account of her life and career. The latter includes being rejected by record labels for sounding “too black” before going on to sell 780,000 copies of her hit “Downhearted Blues.”

Despite colorful anecdotes — including the time Smith faced down Klansmen — Angelo Parra’s book is little more than a narrative bridge between musical numbers, which Braden thankfully delivers in powerhouse fashion. Her rendition of “I Ain’t Got Nobody” is haunting, while “St. Louis Blues,” featuring a lascivious duet with her sax player, perfectly captures Smith’s notoriously earthy side.

Like many of its predecessors, the show is essentially an expanded cabaret act. But Braden channels Smith’s personality and vocal style so winningly and well, you’ll hardly mind the absence of alcohol.