An inside-forward, he played for Ilford in the Isthmian League before signing for Crystal Palace in 1919. He failed to make the first team and in 1920 he was signed by Syd King, the manager of West Ham United. He was moved to wing-half and became a regular in the 1920-21 season. Bishop joined a team that included Syd Puddefoot, George Kay, Edward Hufton, Jack Tresadern, Vic Watson, Jack Young and Billy Henderson.
West Ham United enjoyed a good FA Cup run in the 1922-23 season beating Hull City (3-2), Brighton & Hove Albion (1-0), Plymouth Argyle (2-0), Southampton (1-0) and Derby County (5-2) to reach the final against Bolton Wanderers. The final took place at Wembley Stadium, only four days after the stadium had been completed.
The stadium had a capacity of 125,000 and so the Football Association did not consider making it an all-ticket match. After all, both teams only had an average attendance of around 20,000 for league games. However, it was rare for a club from London to make the final of the FA Cup and supporters of other clubs in the city saw it as a North v South game. It is estimated that 300,000 people attempted to get into the ground. Over a thousand people were injured getting in and out of the stadium. When the game eventually got started, Joe Smith and David Jack scored in Bolton's 2-0 victory over West Ham United.
West Ham United finished in 13th place in their first season in the First Division. Moore ended up as the club's top scorer with 9 goals. The club continued to struggle in the top division and Bishop struggled to hold his place in the first-team and in 1926 he was transferred to Leicester City.
Bishop's form at his new club as inside-forward was so good that he was selected to play for England against Scotland on 2nd April 1927. England won the game 2-1. The following month he won international caps against Belgium (9-1), Luxemboug (5-2) and France (6-0). Despite being on the winning side in all four internationals he failed to win anymore caps.
Sid Bishop died in January 1949.