Born in Atlanta, Georgia, Bonnyman's family moved to Knoxville, Tennessee, when he was a baby. He studied engineering and played football at Princeton, but dropped out his sophomore year and signed up for the Army Air Corps. He was discharged three months later for lack of proficient flying skills, though his character was rated as "excellent." He worked in the coal industry before moving to New Mexico, where he started his own copper mining business.
At the outbreak of the war, Bonnyman enlisted in the U.S. Marine Corps as a private. On November 22, 1943, Bonnyman led a team of 21 Marines in an assault on a bombproof shelter held by Japanese soldiers on the atoll Tarawa. After an intense exchange of fire, his team was forced to withdraw to replenish its supply of ammunition and grenades. Bonnyman then continued his attack and gained the top of the structure, flushing out over one hundred of its occupants into the open. When the enemy returned fire, Bonnyman stood on the forward edge of the position and killed three of the attackers but was killed himself as he urged his men forward. Thirteen of Bonnyman’s original 21 Marines survived.
He was awarded the Medal of Honor in 1947. Frances, his 12-year-old daughter, accepted the award on his behalf. His remains were buried with those of 36 other men at Betio Atoll. They were exhumed in 2015 and repatriated to the United States. He was interred with full Military Honors at West Knoxville's Berry Highland Memorial Cemetery in Tennessee, with a memorial marker at Santa Fe National Cemetery.