Bishop was the leadoff hitter for the last three American League pennant-winning Philadelphia Athletics teams of Connie Mack. Nicknamed "Tilly" or "Camera Eye" for his notable ability to judge pitches, Bishop was adept at working counts and drawing walks, as evidenced by his .423 career on-base percentage, in front of Athletics sluggersAl Simmons, Mickey Cochrane and Jimmie Foxx. Eight times he collected 100 walks, leading the AL with 128 in 1929; twice walked eight times in a doubleheader, to set a major league record; twice draw five walks in a single game, to become the only major leaguer to do this twice and recorded a 2.55 walk-to-strikeout ratio (1153-to-452), as his walk percentage of .204 is only surpassed by Ted Williams's .207. He also scored 100 or more runs during four consecutive seasons (1928–1931), with a career-high 117 in 1930. Rated as one of the best fielders in the game, Bishop led AL second basemen four times in fielding percentage and played 18 World Series games without committing an error. When Bishop scored 117 runs in 1930, he became the only man in major league history to score at least 70 runs while collecting more runs than hits.
After that, Bishop served as baseball head coach at the U.S. Naval Academy between 1938 and 1962. During his 25 years as Navy Midshipmen coach, he posted a 306–143 record, including an academy seasonal record of 24 victories and two defeats in 1961.
Bishop died in his home of Waynesboro at age 62. The baseball stadium at the Naval Academy is named for Bishop.