Bruce first played for Gala YM and then Gala.[2]
The Berwickshire News and General Advertiser of 1 February 1955 notes:[3]
There will be no early return of Norman Bruce as a regular player for Gala. The popular Gala hooker, who is now a sergeant in the R.A.O.C., has signed on with the Army for a 22-year engagement. Bruce has been doing well in Army Rugby and is hooking for an Army XV. against the Civil Service in a side which includes seven internationalists. One of his props will be Hughie McLeod, the Hawick cap. The permanent loss of Bruce is a big blow to the Netherdale club.
He played for Blackheath.[4][5][6] He brought the Blackheath side back to Gala shortly after he moved to England and they won the Gala Sevens that year.[7] While he was back in Galashiels he managed to sneak in a match for Gala YM over Hawick YM in the Border Junior League.[7]
He then played for the Army Rugby Union.[4] He played for the Royal Army Ordnance Corps, captained the Army side, and played for Combined Services.[8]
He then played for London Scottish.[4][9]
He played for South of Scotland District in 1955.[10]
He played for Whites Trial against Blues Trial in 1957, while still with Blackheath.[5]
After impressing in that trial match he was selected for Scotland Probables against Scotland Possibles two weeks later.[6]
He played for Hampshire.[8] The Hampshire County side usually played him out of position as a prop, though he did captain the side.[11]
He was capped by Scotland 31 times between 1958 and 1964.[12]
He played for the Barbarians in 1957.[13]