Shortly after her college graduation, Bosworth became a member of the Actors Studio in Manhattan, where she studied under master teacher Lee Strasberg. Arthur Penn cast her as the lead in her first professional play, a pre-Broadway tryout of James Leo Herlihy’s Blue Denim, about the consequences of teenage pregnancy and abortion. Bosworth appeared in several Broadway shows during the 1950s and 1960s, including Inherit the Wind, Small War on Murray Hill (directed by Garson Kanin), and Jean Kerr's Mary, Mary (where she understudied from 1961-1965 before being cast as the lead for the end of the play's run). She played Elaine Stritch's sister in the drama The Sin of Pat Muldoon and a motormouthed teen based on the young Nora Ephron in Phoebe Ephron's comedy Howie. During this period Bosworth also toured in The Glass Menagerie, playing Laura to Helen Hayes's Amanda, and Remains to be Seen opposite Tommy Sands. She worked regularly on popular television series including Naked City, The Secret Storm, Young Dr. Malone, and The Patty Duke Show. Bosworth can also be seen in the film Four Boys and a Gun as James Franciscus's wife, and as a disgruntled redhead in the audience of Bert Stern’s 1960 cult documentary Jazz on a Summer's Day, about the 1958 Newport Jazz Festival.