Bancroft was born Anna Maria Louisa Italiano in the Bronx, New York, the daughter of Mildred (nee DiNapoli), a telephone operator, and Michael Italiano, a dress pattern maker. Her parents were both children of Italian immigrants. She attended the American Academy of Dramatic Arts, the Actors Studio, and the American Film Institute's Directing Workshop for Women at UCLA. After appearing in a number of live television dramas under the name Anne Marno, she was told to change her surname for her film debut in Don't Bother to Knock in 1952.
