She grew up in Chicago; Westport, Connecticut; Washington, DC; Virginia; North Carolina; and New York City.

She met the playwright Horton Foote, who offered her a job as an understudy in his play Only the Heart, which enabled her to join the Actors' Equity Association and thus become a professional actress.

[2] After coming to the attention of the producer Hal Wallis, Drake was pressured by her agent to sign a Hollywood contract.

She returned to New York City and, in 1947, read for the director Elia Kazan for the lead role in the London company of the play Deep Are the Roots.

Drake wrote the original script for the film Houseboat (1958) under a pseudonym, basing it on an unpublished story she had written.

Drake was a director of psychodrama at the UCLA Neuropsychiatric Institute, worked at Cedars-Sinai Hospital, and maintained a private therapy practice.

She boarded it along with dozens of other wealthy travelers and tourists, at Gibraltar, which was one of many stops the ship made between her home port of Genoa and her final destination of New York City.

When the SS Andrea Doria collided with the Stockholm, Drake waited with the other passengers for rescue, as the ship's severe list rendered half of its lifeboats useless.

She was among more than 1600 people rescued from the ship by the famed French passenger liner SS Île de France.