Born as Joan Letitia LaCock in Logan, West Virginia, Dru came 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).
Before moving to Hollywood, Dru met and married popular singer Dick Haymes in 1941. She was 19 years old. The couple had three children: Richard Ralph Haymes (born July 24, 1942), Helen Joanna Haymes (born May 13, 1944), Barbara Nugent Haymes (born September 19, 1947). Divorced from Haymes in 1949, Dru married Red River and All the King's Men co-star John Ireland less than a month later. The pair divorced in 1957. She had no children from her marriage to Ireland, or subsequent two marriages.
She gave a well-received performance in the dramatic film All the King's Men (1949) and co-starred with Dan Dailey in The Pride of St. Louis (1952), about major-league baseball pitcher Jerome "Dizzy" Dean. She appeared in the James Stewart drama Thunder Bay in 1953 and then a Martin and Lewis comedy 3 Ring Circus (1954). Her film career petered out by the end of the 1950s, but she continued working frequently in television, most notably as "Babs Wooten" on the 1960-61 sitcom, Guestward, Ho!.
After Guestward, Ho!, she appeared sporadically for the rest of the 1960s and the first half of the 1970s, with one feature film appearance, in Sylvia (1965), and eight television appearances.
She was a staunch Republican and appeared at a 1968 GOP cocktail party fundraiser for Richard Nixon.
She died in Los Angeles, California, September 10, 1996, aged 74, from a respiratory ailment that developed from lymphedema, a swelling of the extremities. Her ashes were scattered into the Pacific Ocean.