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. He was nominated for Vezina Trophy and finished third in voting. 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.