Starting in Scottish football Bob Stewart played for Exeter City in the early-1920s having signed from Oldham Athletic. He later played for Wigan Borough.

Bob was playing for Broxburn United of the Scottish Central League before moving to Everton and on to Oldham Athletic at the end of the Great War. Making 34 league appearances for the Boundary Park club, he was released in 1921 to sign for Exeter City. 

Making his debut for the Grecians in the 4-0 defeat at Charlton Athletic on the opening day of the season on 27 August 1921, Bob was out of the side after five matches before enjoying a long run between December 1921 and early April 1922. Totalling 25 league appearances, but not featuring in the final six games, he returned to Lancashire for the 1922/23 campaign when he made three appearances for Wigan Borough.