Bookman represented numerous football clubs, moving from Belfast Celtic to English club Bradford City in 1911. Three years later he switched to West Bromwich Albion, before the First World War led him to return to Ireland to play for Glentoran and then Shelbourne. He won the County Antrim Shield with Glentoran and helped Shelbourne to a Leinster Cup and league win in 1918–19. He returned to the Football League of England to sign for Luton Town in 1919, and played over 100 games for the club before joining Port Vale in September 1923. He returned to Shelbourne the following year. He also won four caps for Ireland, and helped the Irish to claim victory in the 1914 edition of the British Home Championship.