Voss began his career in 1961.[5] He joined the Professional Rodeo Cowboys Association in 1973 and appeared at the National Finals Rodeo in 1974 and 1978.[6] He initially retired in 1978 due to numerous knee injuries throughout his career, but returned the very next year when the Wrangler bullfighting competitions initiated.[7] He would go on to win the Wrangler bullfighting world championship in 1982.
In 2015, he was inducted as a member of the inaugural class into the Bull Riding Hall of Fame.[9] That same year, he was inducted into the Central Texas Cowboy Hall of Fame.
In 2016, he was inducted as a member of the inaugural class into the All Cowboy & Arena Champions Hall of Fame.[10]
In 2017, he received the South Central Texas Rodeo Ring of Honor.