He was a pitcher over parts of three seasons (1886–1887, 1889) with the Pittsburgh Alleghenys and Chicago White Stockings.

For his career, he compiled an 0–4 record in seven appearances, with a 9.96 earned run average and nine strikeouts.

There is disagreement about the year of Bishop's birth.

Retrosheet and Baseball-Reference list his year of birth as 1864, whereas Fangraphs lists his birth year as 1869.

If Fangraphs is correct, Bishop was one of the youngest players in Major League Baseball history, making his debut at roughly 16 years, nine months old.