Bishop was born in Lewisham in 1925, and attended Roan School for Boys in Greenwich. After leaving school, he joined the Royal Navy as a Volunteer Reserve, but impressed while in training and became qualified as an air engineering officer in 1944. Bishop left the Navy in 1946, but maintained his new interest in engineering and achieved a BSc (Eng) from University College, London, and then a PhD from Stanford University, California in 1951. Bishop became a Fellow of Pembroke College in 1954 and lectured at the University. In 1957 he returned to UCL as a department head and then research professor. In 1981 he became vice-chancellor and principal of Brunel University in Middlesex. Bishop received many honours and awards, published widely, and made many advances in theories and practices of engineering throughout his life and career. He died in Portsmouth in 1989.