Bishop previously played for the St. Louis Blues, Ottawa Senators, Tampa Bay Lightning, Los Angeles Kings, and Dallas Stars of the NHL.

Nicknamed "Big Ben", Bishop is the tallest goaltender ever to play in the NHL, along with Mikko Koskinen, Mads Søgaard, Ivan Fedotov, and Dennis Hildeby at a height of 6 ft 7 in (2.01 m).

As a junior in the 2007–08 NCAA Men's Division Hockey competition, Bishop played behind a less-than-stellar team, but had an impressive personal season performance, posting a 2.43 GAA and a .920 save percentage.

On March 11, 2008, it was announced he had signed with the Blues, where he would play the remainder of the season for their American Hockey League (AHL) affiliate, the Peoria Rivermen.

[11] On October 24, he made his NHL debut, coming off the bench in relief of the injured Manny Legace to start the second period, giving up two goals over the final 40 minutes in a 4–0 loss to the Los Angeles Kings.

In his third game played of the season, he would record his first NHL shutout, which came against the Edmonton Oilers at Rexall Place on February 25, 2011, stopping all 39 shots in a 5–0 win.

[17] A kitchen accident resulted in Senators' starting goaltender Craig Anderson being injured indefinitely with a hand laceration, a situation that may have hastened Bishop's move to Ottawa.

[18] At the time of the trade, Bishop was the AHL's top goaltender with a 24–14–0 record, a 2.26 GAA, a .928 save percentage and an AHL-leading six shutouts through 38 games.

[14] Due to the 2012–13 NHL lockout, Bishop began the 2012–13 season in the AHL with the Binghamton Senators, where he posted an 8–3–2 record and 2.59 GAA in 13 games.

[20] However, his play improved as he was named the NHL's Third Star of the Week on February 25, 2013, after posting a 2.03 GAA and .931 save percentage, as Ottawa won all four of its games.

[22] Bishop set a career high and Tampa Bay franchise record on January 19, 2014, by making 48 saves in another victory over Carolina.

[24] Bishop was nominated for the Vezina Trophy—NHL's top goaltender—for the season due to his stellar play in net, though he ultimately finished third in voting.

He had to be helped off the ice that would end his 2013–14 season, as Tampa Bay were swept out of the first round of the 2014 Stanley Cup playoffs by the Montreal Canadiens.

[32] On May 29, 2015, Bishop joined Tim Thomas and Patrick Roy as the only goaltenders to post shutouts in two Game 7s in a single playoff year.

Additionally, Bishop became the first goaltender to win back-to-back playoff shutouts in Madison Square Garden, which would cause the New York Rangers to lose their first Game 7 at home in their franchise's history.

[44] On October 25, 2016, Bishop's two front teeth were knocked out by the Toronto Maple Leafs' Peter Holland on a shot to his mask.

After a deal with the Calgary Flames involving a contract extension fell through, Bishop began the 2016–17 season with Tampa Bay.

[47] As the Lightning dealt with lingering salary cap space concerns sitting outside of a playoff spot, Bishop was traded three days before the NHL trade deadline on February 26, 2017, to the Los Angeles Kings in exchange for goaltender Peter Budaj, defenseman Erik Černák, a 2017 NHL entry draft seventh-round pick and a conditional second-round pick in 2017.

[48] Bishop made his debut with Los Angeles on February 28, a 2–1 overtime loss in which he stopped 28 of 30 shots and was awarded the game's third star.

[51] On March 14, 2019, in a game against the Minnesota Wild, Bishop broke Ed Belfour's franchise record for longest shutout streak before being pulled due to a lower body injury.

[53] In the 2019–20 season, Bishop was able to reach his second career Stanley Cup Finals appearance, and first with the Dallas Stars, albeit deemed "unfit to play" throughout the majority of the playoffs.

[54] On June 10, 2022, Bishop's contract along with a seventh-round draft pick in 2022 were traded to the Buffalo Sabres in exchange for future considerations.