Cowdenbeath, Fife born inside right George Bissett began his football career before the First World War with Glencraig Thistle and joined Third Lanark in 1916. In March 1918 he went on loan to St Mirren, playing twice for The Buddies before returning to Thirds, but after the end of the War he signed for First Division Manchester United, making his Football League debut against Burnley in October 1919. He stayed two years at Old Trafford, scoring 10 goals in 42 games before a move to Second Division Wolverhampton Wanderers in November 1921.
His first season at Wolves was successful, with 9 goals in 26 appearances, however the appointment of George Jobey as manager during the 1922-23 season saw Bissett’s opportunities decline and he featured only sporadically in that campaign. After 10 goals in 44 appearances for Wolves, he left to join Welsh League club Pontypridd in January 1924, but moved to Southend United four months later, where he was a regular for two seasons, scoring 18 goals in 66 matches for The Shrimpers. He then returned to Scotland in the 1926 close season where he had a brief spell with Lochgelly United before joining Dunfermline Athletic later the same year before his retirement.