Bellmon was born near Billings, Oklahoma. He graduated from Oklahoma A & M (now Oklahoma State University) in 1942 with a Bachelors Degree in agriculture. He was a lieutenant in the United States Marine Corps from 1942 to 1946. He was a tank platoon leader in the Pacific Theater of World War II. He took part in four landings on Pacific islands, including Iwo Jima. For his service, he was awarded the Legion of Merit and a Silver Star. After the war he returned to farming and took up politics.

He served a single term in the Oklahoma legislature (1946-1948). In 1960 he served as the State Republican Party Chairman. He served as Governor of Oklahoma from 1963 to 1967. While governor he served as the chairman of the Interstate Oil Compact Commission and as a member of the executive committee of the National Governor's Conference. Under Oklahoma law at the time, he was not able to run for second term. He was elected to the U. S. Senate in 1968 and reelected in 1974. He did not run for a third term in 1980. His seat was won by Republican Don Nickles. He was a cofounder and cochairman of the Committee for a Responsible Federal Budget. He was appointed the interim director of the Oklahoma Department of Human Services in 1983. In 1986 he was once again elected Governor of Oklahoma. During his second tenure as Governor he chaired the Southern States Energy Board. He has taught at Oklahoma City University, Central State University, Oklahoma State University, and the University of Oklahoma.