Before playing in the NHL, Bishop played parts of 1 season with the Texas Tornado of the North American Hockey League (NAHL) and 3 years of college hockey with the University of Maine Black Bears. With the Tornado, Bishop led them to their second National Championship and Gold Cup and he was named to the first team of the NAHL All-Rookie Team. With the Black Bears, Bishop was named the Rookie of the Month in the months of October 2005 and February 2006. He was also named the Goaltender of the Month by the NCAA's Hockey East conference. He led Maine to the Frozen Four twice. In 2006, they lost in the semi-finals to the University of Wisconsin–Madison and in 2007, they lost to Michigan State University in the semi-finals.
He was drafted 85th overall by the St. Louis Blues in the 2005 NHL Entry Draft. On March 11, 2008, Bishop signed a two-year entry-level contract with the Bruins.[2] He began playing for their AHL-affiliate, the Peoria Rivermen.
The Blues called Bishop up on October 19, 2008.[3] On October 24, 2008, Bishop played in his first NHL game, coming off the bench to replace an injured Manny Legace to start the second period. He gave up two goals in a 4–0 loss to the Los Angeles Kings.[4] On February 25, 2011, Bishop recorded his first NHL shutout, stopping 39 shots in a 5–0 win against the Edmonton Oilers.[5]
On April 3, 2013, the Senators traded Bishop to the Tampa Bay Lightning in exchange for Cory Conacher and a fourth-round draft pick.[8] Bishop signed a two-year, $4.6 million extension with the Lightning on April 15.[9]
On January 19, 2014, Bishop set both a career high and a Tampa Bay franchise record after he made 48 saves in a 7–3 victory over the Carolina Hurricanes.[10][11]
The Lightning named Bishop the starting goaltender over Anders Lindbäck for the 2013–14 NHL season. Over the season, Bishop recorded a record of 37–14–7 over the 63 games played that season. He recorded a .924 save percentage, a 2.23 goals against average, was ranked fourth in games played, as well as seventh in save percentage and goals against. He posted five shutouts, the second-most in Lightning history, and he set single season records for wins, save percentage and GAA. He recorded the second-most saves in Lightning history, with 1,625.[12] He was nominated for Vezina Trophy and finished third in voting.[13] On April 4, 2015, Bishop recorded his 38th win of the season in a 4–0 shutout win against the Florida Panthers. This beat the Tampa Bay franchise record he set the previous season and was a new personal best.[14]