Jed Bernstein's Above the Title Entertainment is producing the reading at the Westside Theatre.
Mark Waldrop directs a cast that includes Foster and Swenson as well as Marc Kudisch, Debra Monk and Christopher Sieber.
The musical, which premiered last year at the New York Musical Theatre Festival, features a libretto by Hunter Foster and a score by Rick Crom.
Bonnie & Clyde: A Folktale, according to press notes, is described as such: "America's most romantic gangsters, Bonnie & Clyde, outwit and outrun a relentless (yet always ladylike) J. Edgar Hoover to the delight of the poor and downtrodden, as their relationship changes from 'strictly business' to reluctant love."