Bochner was born in Pittsburgh in 1940. In high school, he won early recognition for his talent from The Scholastic Art & Writing Awards and studied with Joseph Fitzpatrick]. He studied art at Carnegie Mellon University and graduated in 1962. After leaving Pittsburgh, he studied philosophy at Northwestern University near Chicago. He moved to New York in 1964 and worked as a guard at The Jewish Museum. In 1966, he was recruited by the influential art critic Dore Ashton to teach art history at the School of Visual Arts in New York.