The production will continue through May 18.
Draper specialized in character-driven monologues, which she first performed in drawing rooms. Despite the idea that performing onstage was not considered acceptable in her time, Draper pursued a successful career onstage. Her work is credited as inspiring Lily Tomlin, John Lithgow, Tom Waits, Charles Busch, Julia Sweeney, Simon Callow and Charles Nelson Reilly.
"I am in awe of Ruth Draper,” Bening said in a statement. "Performing these monologues is a great honor for me, and I look forward to the formidable challenge of breathing life into these stunning pieces."
The production will feature some of Draper's well-known works, including The Italian Lesson, Doctors and Diets, A Debutante at a Dance and A Class in Greek Poise.
Bening is a four-time Academy Award nominee for her work in "The Grifters," "American Beauty," "Being Julia" and "The Kids Are All Right." The Tony Award nominee's stage work includes Coastal Disturbances, The Cherry Orchard, Talking Heads, Hedda Gabler, Medea and The Female of the Species.
Tickets and more information are available by calling (310) 208-5454 or visiting geffenplayhouse.com.