Born Joanne Letitia LaCock in Logan, West Virginia, Dru came to New York City in 1940, aged 18, and after finding employment as a model, was chosen by Al Jolson to appear in the cast of his Broadway show Hold Onto Your Hats. During this time Dru met and married the popular singer, Dick Haymes, and when they moved to Hollywood she found work in theater. Dru was spotted by a talent scout and made her first film appearance in Abie's Irish Rose (1946).

Over the next decade she appeared frequently in films, most often cast in westerns such as the John Wayne films Red River (1948) and She Wore a Yellow Ribbon (1949). She also gave a well received performance in the drama film All the King's Men (1949). She later lamented that she had been typecast in western films, commenting that once an actress became typecast, that was the end, and adding that she had never liked horses. Her film career began to fade by the end of the 1950s but she continued working frequently in television.

Although regarded as a capable and popular film actress, it was for her contributions to television that Dru was awarded a star on the Hollywood Walk of Fame.

She died in Los Angeles, California at the age of 74 from lymphedema, a disease "which is especially common after surgery or radiation therapy were used in combination to treat cancer", which indicates that she probably had undergone these treatments for cancer (likely breast cancer) prior to her death.