Bishop attended Gettysburg College and studied medicine at Harvard University. In 1962 he secured an internship at Massachusetts General Hospital in Boston, and in 1964 he moved to the National Institutes of Health, Washington DC, as research associate in virology, later becoming senior investigator (1966) and assistant professor (1968). He was appointed professor of microbiology and immunology at the University of California Medical Center, San Francisco, in 1972, and in 1981 he became director of the G. W. Hooper Research Foundation.

Bishop, working in collaboration with Harold Varmus, demonstrated for the first time that cancer-causing genes (oncogenes) carried by certain viruses are derived from normal genes present in the cells of their host, known as proto-oncogenes. This work by the team at the University of California, published in 1976, led to the discovery of many more such cellular genes, and represented a major advance in cancer research. In recognition of this, Bishop and Varmus were jointly awarded the 1989 Nobel Prize for physiology or medicine.