Price was born in Laurel, Mississippi. She studied at Central State College, Wilberforce, Ohio, and with Florence Kimball at the Juilliard School of Music in New York City. She began her professional career in 1952, when she appeared as Bess in George Gershwin's "Porgy and Bess" on Broadway, followed by an international tour. She made her recital debut in New York City in 1954, and appeared in a television production of "Tosca" for NBC in 1955. 