Hubbard was born in New York City to Elizabeth Wright Hubbard and Benjamin Alldritt Hubbard. Her mother, a physician, was a pioneer in homeopathy and one of the first women to earn a medical degree from Columbia University. She had two brothers, Theodore and Merle, an opera talent manager. Elizabeth attended Radcliffe College, and graduated summa cum laude. She pursued her theatrical education at the Royal Academy of Dramatic Art in London, where she was the first American to receive the school's silver medal. She was married to furrier David Bennett from 1970 to 1972; they had one child, a son, Jeremy Bennett (born September 20, 1971).