Bosseler was a four-year starter at fullback for the University of Miami. In his senior year, 1956, he helped the team to an 8-1-1 record, was named All-America by the Associated Press, and was MVP in the Senior Bowl. He rushed for 1,642 yards in his four years.
Bosseler was drafted ninth overall in the 1957 NFL Draft and played for seven seasons with the Redskins before retiring. He was a one-time Pro Bowler in 1959.
After his football days, Bosseler joined Prudential Bache in Miami and became a vice-president.