Born in Senegal to Sierra Leonean Aku parents in 1919, Abdul Rahman Bassir was raised in Fourah Bay area, in the municipality of Freetown, by his parents Abdul and Isatu Bassir. He attended the Prince of Wales Secondary School where he passed the Senior Cambridge examination with exemption from London matriculation. In 1946 after a short teaching spell at the prestigious Bo Government Secondary School he went to Yaba College where he obtained the Higher National Diploma. He went to the United Kingdom, where he earned the Bachelor of Science degree in 1949 and PhD in 1951 from Liverpool University.

He spent most of his professional career at the University of Ibadan, where he founded the Biochemistry and Microbiology departments. He laid the foundation of what became the first medical school in West Africa. By 1958, he was already a full professor. His academic specialty was nutrition and biochemical toxicology. He was at various times Head of those two departments, Dean of faculty and also served as acting Vice Chancellor.

He had written at least 250 professional papers by 1972 when University of London conferred the coveted doctor of science degree (D.Sc.) on him. He had performed very successful lecture tours in the then Soviet Union, the United Kingdom, and the United States of America among others.

Olumbe Bassir was the author of several books. His 1957 book Anthology of West African Verse was seminal in introducing written African poetry to Western audiences. His other popular books include Handbook of Practical Biochemistry (1963) and Metabolism of Afflatoxins and other Mycotoxins (1989).

In 1968, he formed a partnership with Tecwyn Williams through the British Inter-University Council for Higher Education Overseas. The programme's research division helped developed the Drug Metabolism and Biochemical Toxicology research program at Ibadan and contributed in fostering interest and making interesting findings in animal nutritional habits.

After retiring from the University of Ibadan, he remained active for several years, continuing to act as editor of the West African Journal of Biology and Applied Chemistry. He also served as chairman of the Welcome Nigeria Fund, which became the Bassir-Thomas Biomedical Foundation in the early 1990s. He also regularly organised the annual Open House Colloquim.

Advocacy and Activism
Olumbe Bassir was a lifelong advocate for peace, and was an active member of the Pugwash Conferences on Science and World Affairs. He also contributed to the Universities and the Quest for Peace. He was also sympathetic to the Fabian Society which he flirted with in his student days in England. He founded the Association of University Teachers in Nigeria which later became the Academic Staff Union of Universities. Despite being non-partisan, he helped develop the manifesto of the Action Group.

Personal life
His name "Olumbe" means "the Lord exists" in Yoruba. He married Constance while still resident in the UK. He had 12 children. In 2000, he suffered a blood clot in the brain due to a traumatic injury to the head. Despite successful surgery and recuperation he died at Ibadan on May 23, 2001.