Barrett began taking acting classes as a child. She attended Shaker Heights High School, graduating in 1950 before going on to the University of Miami in Coral Gables, Florida, then had some stage roles and came to Hollywood. Her father, william Hudec, was a Cleveland police officer. He was killed in the line of duty in 1955 while Barrett was touring with an off-Broadway road company. She was briefly seen in Will Success Spoil Rock Hunter? (1957) in an ad parody at the beginning of the film, and had roles in a few movies, including Love in a Goldfish Bowl (1961), Sylvia (1965), A Guide for the Married Man (1967), and Track of Thunder (1967). She worked at the Desilu Studios on several TV shows, including Bonanza, The Untouchables, The Lucy Show, and The Lieutenant (produced by Gene Roddenberry). She received training in comedy from Lucille Ball. In 1960, she played Gwen Rutherford on Leave It to Beaver.