Bernstein studied chemical engineering at the City College of New York (Baccalaureate 1944) and in 1950 received his PhD from New York University with his thesis entitled "Improved Calculations on Cascade Shower Theory". From 1950 to 1954 he worked at the Westinghouse research laboratories. From 1954 to 1964, he was a scientist at the Princeton Plasma Physics Laboratory, where he was an participant as a Senior Scientist in Project Matterhorn when the project involved secret U. S. government research on magnetic fusion. In 1964, he became a Professor for Applied Physics at Yale University, where he was from 1994 "Carl A. Morse" Professor for Mechanical Engineering and Applied Physics. In 2004 he retired with the rank of professor emeritus. He was a research consultant with the research laboratories of United Technologies and RCA, the Los Alamos National Laboratory, and the Naval Research Laboratory. He was a member of the Fusiona Policy Advisory Committee and the Consulting Committee for Fusion Energy at the U. S. Department of Energy.
^Biographical data from Lisl Goodman: Death and the creative life: conversations with prominent artists and scientists, Springer 1981 and Burning Plasma: bringing a star to earth, National Research Council