Kilmarnock born outside right Bobby Muir began his football career with Kilmarnock Deanpark in 1895 and joined Scottish League Clyde in 1896 before returning to his home town to join Kilmarnock in 1897. He moved south to join Southern League Bristol Rovers in 1901, spending 2 years at Eastville before he joined Celtic in May 1903.
He made his competitive first team debut for The Bhoys in a 2-1 Scottish League win over Partick Thistle at Parkhead on August 15th 1903. That game is best remembered as being the occasion Celtic wore their now world famous green and white hoops for the very first time. Muir was in great form during the 1904 Scottish Cup Final when he helped Celtic defeat Rangers 3-2. He was said to be “the best man in his position since Neil McCallum… a bewilderer with lean and clever footwork”. In the League, things weren’t as easy, and Celtic finished in fourth place, joint on 38pts with Rangers as Third Lanark took the title five points ahead.
After just one season in Glasgow he was tempted back to England and joined First Division Notts County in April 1904 after seven goals in 25 appearances for Celtic. He made his Football League debut against Everton that September and made 20 appearances for The Magpies as they finished 18th in the League. But after only one season he returned to the Southern League joining Norwich City, for whom he played for the next three years. He retired in 1908 due to back problems and later moved to Canada, playing for Canadian club Toronto Eatonia, and he later acted as Secretary and Treasurer of the Ontario FA.