Born at Ansley, Nebraska, Bonner graduated in chemistry from the University of Utah in 1931 but turned to biology under the influence of Theodosius Dobzhansky. He received his PhD from the California Institute of Technology in 1934, which was then becoming known as the main center for molecular biology. Here he became interested in developmental biology and the question of why only some genes of the chromosome complement of an organism are expressed in any one cell. He discovered that histone, a protein that is found associated with the chromosomes, is responsible for shutting off gene activity, and that if the histone is removed then the repressed genes become functional again. He also discovered that certain hormones act by repressing and derepressing genes.

Bonner in addition conducted research on the artificial synthesis of ribonucleic acid and studied ribosomes and mitochondria. From 1946 to 1981 he was professor of biology at Cal Tech, becoming Professor Emeritus in 1981. He wrote many books, including The Nucleohistones (1964) and The Molecular Biology of Development (1965).