After graduating from high school in Frederick, Oklahoma in 1941, Bobby entered University of Tulsa to play football for coach Henry Frnka. A fullback, Dobbs played in Tulsa's first ever bowl game; the 1943 Sugar Bowl. With the United States involved in World War II, Bobby's patriotism, along with his desire to become a pilot and play football, led him to West Point. In early 1943, he joined the United States Army Air Corps. His athletic ability resulted in letters in football and basketball. Bobby was the starting fullback on the 1944 Army team. The 1944 Army team had a 9-0 record, two future Heisman Trophy winners (Doc Blanchard & Glenn Davis), and defeated their opponents by a combined score of 504-35 en route to winning the Associated Press National Championship.