Bidwell was drafted by the Green Bay Packers in the fourth round of the 1999 NFL Draft. He was diagnosed with testicular cancer on September 1, 1999 and was placed on the reserve/non-football illness list on September 5. In 2000, Bidwell beat out Tom Hutton for the starting punting job. He went on to start in all 16 games for nine consecutive seasons, from 2000 to 2008. He was re-signed to a one-year contract worth $605,000 on April 30, 2003.
Bidwell was signed to a three-year contract by the Tampa Bay Buccaneers on March 13, 2004. He was selected to the 2006 Pro Bowl following the 2005 season. On November 27, 2006 he signed a contract extension with the team. He was placed on injured reserve due to a hip injury on August 17, 2009. He was released on March 4, 2010.