Bishop was drafted by the Atlanta Braves in the 36th round of the 2012 Major League Baseball draft out of high school, and by the Seattle Mariners in the 3rd round of the 2015 Major League Baseball draft out of college. He played in 2015 for the Everett AquaSox of the Class A- Northwest League, batting.320 /.367/.393 with 13 steals in 16 attempts, and led the league with 12 HBP and 11 sacrifice hits. In August 2015 MLBPipeline.com ranked Bishop as the Mariners' #14 prospect. He was named Northwest League Player of the Week on August 24, 2015, a Northwest League Post-Season All Star, and an MILB.com organization All Star. In 2016, Bishop played for the Clinton LumberKings of the Class A Midwest League, and the Bakersfield Blaze of the Class A+ California League, batted a combined.273/.338/.326 with 8 steals in 9 attempts, and was named a California League All Star. MLBpipeline.com ranked him the #9 Mariners prospect. In February 2017 MLB.com ranked him the #6 Mariners prospect, the best defensive player in the organization, and tied for the best runner in the organization. Bishop began 2017 with the Modesto Nuts of the California League, batted.296/.385/.400 with 16 steals in 20 attempts and was the MVP in the mid-season California League All Star Game, and was promoted to the Arkansas Travelers of the Class AA Texas League. In July 2017Baseball America ranked him the #7 2017 mid-season prospect of the Mariners. With Arkansas, he batted.336/.417/.448. In 2017 MLBpipeline.com ranked him the #5 Mariners prospect. The Seattle Times named Bishop the Mariners' 2017 Player of the Year, and he was named the Jewish Baseball News Minor League MVP. He played for the Peoria Javelinas in the Arizona Fall League in the fall of 2017, and was an AFL All Star. In 2018 MLBpipeline.com ranked him the #5 Mariners prospect. Playing for the Arkansas Travelers of the Class AA Texas League, he batted.284/.361/.412 with 70 runs, 8 home runs, and 33 RBIs in 345 at bats.
Seattle Mariners
After the 2018 season, the Mariners added Bishop to their 40-man roster. On March 19, 2019, the Mariners announced that Bishop was included on their Opening Day active roster. Bishop made his MLB debut on March 21 as a defensive replacement in the 8th inning, replacing Ichiro Suzuki in right field during Ichiro's final game. Bishop struck out in his first big league at bat. On March 23, he was optioned to the AAA Tacoma Rainiers.