So while in Scotland, she began to write “Josephine and I,” booking a small pub theater in North London to show the work to family and friends. Somehow a few producers sneaked in, too, and soon several theaters were competing to develop the piece, which Phyllida Lloyd, Ms. Jumbo’s “Julius Caesar” director, asked to oversee. In an email, Ms. Lloyd described working with Ms. Jumbo as “addictive,” citing her gift for language and a “playful fearlessness.” Their retooled “Josephine and I” opened at the Bush Theater in London in 2013. The Daily Mail called it “a mighty performance,” and The Guardian termed Ms. Jumbo “dazzling.” Later in 2013, it won The Evening Standard’s “Emerging Talent” award.

In “Josephine and I,” the Girl explains her lifelong devotion to Baker, performing the occasional cabaret number, if not that banana dance. (Ms. Jumbo has also declined to bring a cheetah to the stage. “I think I might have raised hell if I’d gone to the Central Park Zoo and asked for one,” she said.) The Girl isn’t exactly synonymous with Ms. Jumbo (some of the stories she tells are her own, some, like a harrowing tale of filming a sex scene, are borrowed from friends), but both the Girl and Ms. Jumbo idolize Baker for her bravery, her willingness to reinvent herself, her flouting of restrictions.

Baker, like Ms. Jumbo herself, had little patience for categories or limits. “You read one article that calls her an erotic dancer; you read another article that calls her a Second World War French Resistance spy,” Ms. Jumbo said. “Then you read another article that she adopted 12 children from seven different countries way before Angelina Jolie did.” She added, “You couldn’t make this stuff up.” Baker, who died in 1975, is very much alive to Ms. Jumbo. Though it’s written as a solo piece, she prefers to think of “Josephine and I” as a two-hander. Baker, she said, “is kind of in the show.”

Ms. Jumbo reluctantly admitted that rehearsing “Josephine and I” while still appearing on Broadway had left her somewhat tired. But she described her work on “The River,” Jez Butterworth’s gnomic and elliptical play, as a joy. Her co-star, Mr. Jackman, characterized her in an email as possessed of “a fierce intelligence, a razor sharp wit, a never-ending determination to dive deeper into her work.” Ms. Jumbo, rather less formally, called him, “incredibly funny and a big dork.” She declined, however, to reveal any secrets of that play’s cryptic script, saying, “People shouldn’t think too hard about what it means.”

But she’s been thinking a lot about her own show and the changes it has wrought in her life. Inspired by Baker’s example, Ms. Jumbo has since recommitted to an acting career, but on her own terms. “By the end of the show, I knew exactly who I was, and I knew exactly what I wanted to do in this business,” she said. “And I knew I wasn’t leaving — I wasn’t going anywhere.”

She’s about to film a movie in London and is working on several plays and screenplays, including a story of a 17th-century mixed-race pickpocket, part of her effort to create more roles for nonwhite women. Perhaps some future girl will see them, like Ms. Jumbo saw “Zouzou,” and feel visible, important, beautiful, beloved.

“I guess I’d like to keep writing, and I’d like to keep acting, and I’d like to keep being a happy person,” she said. “I don’t know what my path is going to be yet, but I’m prepared to be brave and hack it out the best way I can.”