Bonner was born in Butte, Montana and graduated from high school in Butte. He received both his undergraduate and law degree from Montana State University, which is now the University of Montana in Missoula. On February 3, 1929 he married Josephine Martin. The Bonners raised five children - four girls (Jo, Jackie, Billie and Pat) and one son, Tom.
After the war, he successfully ran for Governor of Montana as the Democratic Party candidate. He was governor from 1949 to 1953. He was the Delegate to the Democratic National Convention in 1952. After leaving the governorship, Bonner practiced law in Helena. He was a Justice of the Montana Supreme Court from 1968 until his death.