The other finalists are Utah defensive coordinator Gary Anderson, Ball State offensive coordinator Stan Parrish, Florida defensive coordinator Charlie Strong and Oklahoma offensive coordinator Kevin Wilson.
The winner will be announced Dec. 9 at 11:30 a.m. at the Doubletree Hotel in Little Rock, Ark.
TCU (10-2), ranked 11th in the BCS Standings, tops the nation in run defense (48.7 yards per game) while placing second in total defense (215.1 yards per game), scoring defense (10.9 points per game) and sacks (41). The Frogs are fourth in pass defense efficiency (96.1).
Also serving as the Horned Frogs' defensive line coach, Bumpas mentors Jerry Hughes. After coming to TCU as a tailback, Hughes was converted to defensive end. He leads the nation with 14 sacks and six forced fumbles while ranking in the top 10 with 18.5 tackles for loss and three fumble recoveries. He also has two interceptions, including one returned for a touchdown.
Hughes is one of five finalists for the Bronko Nagurski Trophy as the nation's top defensive player. He's also one of 15 "Players to Watch" (and one of just five defensive players) for the Walter Camp Football Foundation's 2008 Player of the Year award.
Bumpas is in his fifth season with the Frogs. In 2006, TCU ranked second nationally in run defense and total defense while placing third in scoring defense. The 2005 Frogs led the nation in turnover margin, interceptions and takeaways.
In a coaching career that has spanned over 30 years, Bumpas has won championships in four different conferences. Later this month, he'll coach in his 14th bowl game.
TCU head coach Gary Patterson was a 2000 finalist for the Broyles Award.