Bowers attended Bamberg-Ehrhardt High School in Bamberg, South Carolina, where he was a three-sport athlete in football and track. He played as a defensive end and running back for the Bamberg-Ehrhardt Red Raiders high school football team. As a senior in 2008, he led the team to an 11–2 record by recording 97 tackles, 33 tackles for loss and 14 sacks on defense, while on offense, he rushed for 1,219 yards and scored 19 touchdowns, he caught two touchdown passes, averaged 40 yards per kickoff return, and blocked seven kicks.
Bowers was ranked the No. 1 overall prospect by ESPN.com in 2008, the first Clemson recruit in history to be ranked as the number-one player in the nation by any recruiting service. Rivals.com dubbed Bowers the top defensive end prospect of the high school classes 2005–2009, describing him as "the closest thing to Reggie White and Bruce Smith". He chose Clemson over Florida State, Georgia, Notre Dame, Ohio State, Penn State, South Carolina, Tennessee, and Virginia Tech.
Bowers graduated early from high school and enrolled at Clemson University in January 2008, where he was a member of the Clemson Tigers football team from 2008 to 2010. He went through 2008 spring drills and had a game-high seven tackles in the 2008 Spring Game. As a true freshman in 2008, Bowers started six of 13 games, finishing the season with 37 tackles including eight for loss. During his second year in 2009, Bowers recorded 46 tackles, 10.5 for loss and three sacks, in spite of an injury that forced him to miss three games.