Burris was born on January 20, 1923, in Nowata, Oklahoma. He was raised in Muskogee, Oklahoma by farmer Paul "Pop" Burris.[1][2] He had five sisters and five brothers. All of his male siblings also played football, with the first three earning letters at Oklahoma: Kurt, Bob, Lynn, Lyle, and Don.[2][3] Buddy Burris attended Muskogee Central High School where he played football. There in 1939, he participated in the football team's 12–0 "Indian Bowl" victory over Daniel Webster High School of Tulsa, Oklahoma.[1]
After the war, Burris returned home with the intent of resuming college. At Tulsa, head coach Frnka had moved onto Tulane and had been replaced by Buddy Brothers. Burris said he liked Brothers, but was angered by one of his assistants who told him he had an obligation to return to Tulsa. Instead, Burris went to Norman, Oklahoma to watch the Oklahoma Sooners practice. First-year head coach Jim Tatum sent Burris onto the practice field where he blocked three punts. Tatum was impressed enough to offer Burris a scholarship the following week.[3]
From 1946 to 1948, Burris played offensive and defensive guard. He was one of many returning war veterans to join the team and among eight future All-Americans in the 1946 recruiting class.[3] Burris became the first Sooner to be named an All-American all three years at Oklahoma. In 1948, he was named a consensus All-American.[4] He was also the first Sooner inducted into the Helms Athletic Foundation Football Hall of Fame.[3] Burris graduated from the University of Oklahoma with a bachelor's degree in business administration.[1]
Burris was selected in the fifth round of the 1947 NFL draft by the Green Bay Packers (31st overall).[6] He played with the Packers for three seasons.[7] In 1949, he saw action in ten games and recorded one interception and recovered one opponent fumble. In 1950, he played in nine games and returned three kickoffs for 18 yards. In 1951, he saw action in seven games and recovered one own team fumble.[8]