Daniels was born Phyllis Virginia Daniels (Bebe was a childhood nickname) in Dallas, Texas. Her father was a travelling theater manager, Scottish-born Melville Daniel MacMeal who changed his name to Danny Daniels after a disagreement with his own father over his ambition to change from the medical profession to show business. Her mother was a stage actress, born Phyllis de Forest Griffin, who was in Danny's travelling stock company when their child was born. At the age of ten weeks her father proudly carried her on stage even though there was no part in the play for a baby. The family moved to Los Angeles, California in her childhood, and she began her acting career at the age of four in the first version of The Squaw Man. The same year, she went on tour in a stage production of Shakespeare's Richard III. The following year, she participated in productions by Oliver Morosco and David Belasco.