Bernstein studied at Harvard University, receiving his bachelor's degree in 1951, his master's in 1953, and his Ph.D. in 1955, on electromagnetic properties of deuterium, under Julian Schwinger. As a theoretical physicist, he worked on elementary particle physics and cosmology. A summer spent in Los Alamos led to a position at the Institute for Advanced Study. In 1962 he became a faculty member at New York University, moving to become a professor of Physics at Stevens Institute of Technology in 1967, a position that he continues to hold as professor emeritus. He has held adjunct or visiting positions at the Brookhaven National Laboratory, CERN, Oxford, the University of Islamabad, and the Ecole Polytechnique.