Born in Logan, West Virginia, Dru moved to New York City in 1940 at the age of eighteen. After finding employment as a model, she was chosen by Al Jolson to appear in the cast of his Broadway show "Hold On to Your Hats". When she moved to Hollywood, she found work in the theater. Dru was spotted by a talent scout and made her first film appearance in "Abie's Irish Rose" (1946). Over the next decade, Dru appeared frequently in films and on television. She was often cast in western films such as Howard Hawks's "Red River" (1948), John Ford's "She Wore a Yellow Ribbon" (1949), and "Wagon Master" (1950).