Bouman initially attended South Dakota State University and transferred to St. Cloud State University in 1992. At St. Cloud State, Bouman lettered in football from 1993 to 1996. In his three years, he passed for 4,354 yards and completed 326 passes (including for 30 touchdowns). In his senior year, Bouman was an honorable mention All-North Central Conference selection. He earned his degree in sports sociology from St. Cloud State in 1997.
Bouman signed as an undrafted free agent with the Minnesota Vikings in 1997. Bouman briefly replaced Daunte Culpepper as the Vikings starting quarterback toward the end of the 2001 NFL season after Culpepper was injured. In a game against the Tennessee Titans, Bouman completed 21 of 31 passes for 384 yards and four touchdowns and was named NFC Offensive Player of the Week. In 2002, Bouman took over again for Culpepper with the Vikings trailing the New York Giants 27-20 but could not complete a potential tying touchdown drive. After the game, Bouman expressed interest in becoming a starting quarterback.
In 2003, the Vikings traded Bouman to the New Orleans Saints as a backup to Aaron Brooks. On December 14, 2005, after a loss on national television to the Falcons, the Saints benched Brooks and announced Bouman as the team's starter for the last three games of the season. The Saints lost all three games. Prior to the 2006 season, Bouman was released by the Saints in favor of Jamie Martin, who would back up newly signed starter Drew Brees.
He was re-signed for a fourth time on September 21, 2010, when the Jaguars placed Luke McCown on the injured reserve. On 5 October 2010, the Jaguars released Bouman. On October 19, Bouman was re-signed after injuries to David Garrard and Trent Edwards. Bouman started for the Jags against the Kansas City Chiefs on October 24. Bouman played well, throwing for 222 yards, and 2 touchdowns, however he also threw 2 interceptions. He was re-signed again by the Jaguars on December 17. Bouman was re-signed once more on August 9, 2011, due to a back injury to starter Garrard. He was released on August 29.