He played junior hockey for the Peterborough Petes from 1981 to 1985 and was chosen 47th overall by the Los Angeles Kings in the 1983 NHL Entry Draft. Turning pro in 1985-86 with the New Haven Nighthawks, Shoebottom was traded to the Washington Capitals in October, 1985. He then spent two seasons in the minors and could not crack the Capitals lineup.
The Boston Bruins signed him as a free agent in 1987. For four seasons Shoebottom played mostly in the minors, but he did get into 35 regular season games with the Bruins (scoring a goal and four assists) and 14 playoff games (with a goal and 2 assists). After leaving the Bruins in 1991 he played three seasons of minor pro and retired in 1994.
He returned as a player-coach of the San Diego Gulls of the West Coast Hockey League in 1995-96. He continued solely as a player in 1996-97 and then played a few games for the Austin Ice Bats in 1997-98 before retiring.