A native of Auburn, Maine, Bower attended Middlebury College in Vermont, where he won the NCAA national championship in Nordic combined in 1961.

After retirement, Bower and his wife Bonnie moved to Park City, Utah, where Bonnie started the Park City Winter School to allow skiers to attend school in the summer while competing in the winter.

Bower's son Ricky (born 1980) won the Snowboarding half-pipe World Championships in Germany in 1999.

In 1999, Sports Illustrated magazine ranked him 19th among Maine's 50 Greatest Athletes of the 20th century.

Other American King's Cup winners include Kerry Lynch (1983), Todd Lodwick (1998), Bill Demong (2009) and Bryan Fletcher (2012).