Bronson moved to Seattle from Wisconsin in 1903 with his parents. They resided at 239 39th Avenue N on Capitol Hill. He attended the University of Washington and played Husky football from 1912 to 1916. He graduated with a degree in forestry and enlisted in the U.S. Army at the beginning of World War I.
On September 26, 1918, Bronson was a member of Company H, 364th Infantry Regiment, 91st "Wild Westerners" Division near Eclisfontaine, France. He was wounded by a hand grenade and then by a bullet and still led his unit to capture enemy positions and capture enemy soldiers. Bronson remained on duty through the night and into the next day. He disregarded instructions to get medical attention and joined another company to continue the assault. When that unit was forced to withdraw because of artillery fire, Bronson was the last man to leave the advanced position.
Other veterans from Seattle led the 11-year campaign for recognition of Bronson's heroism. The awards ceremony was held in the office of President Herbert Hoover (1874-1964) in Washington, D.C. After the war, Bronson became an executive with a paint company in Ohio and New Jersey, and later worked in the family lumber business in Oregon. He died in Oregon in 1957 and was buried at Arlington National Cemetery.