Bulmer was born in Birmingham, England, in 1931. After graduating from Rugby School, he studied at Merton College, Oxford, from 1949 to 1957, taking a B.A. in animal physiology in 1952, a diploma in applied statistics the following year, a D.Phil. in statistics in 1957, and a D.Sc.[3] He then lectured at the University of Manchester from 1957 to 1959, after which he became a lecturer in biomathematics at the University of Oxford. In 1991, he left Oxford to become a professor in the Department of Biological Sciences at Rutgers University, where he remained until 1995.[2]