The Gunn family home in Thurso was a farm, and the young Bryan would often pester the farmhands to play football with him. They would use a turnip if no ball was available. By the age of four he was keen on goalkeeping; he was fearless of injury and enjoyed diving on the ball. When Bryan was four-and-a-half, the family moved to Invergordon, 20 miles from Inverness. He attended Park Primary School in the town and joined the school football team. Future professional Bobby Geddes was favoured over him as first-choice goalkeeper for the team; Gunn played as an outfield player until Geddes moved on to secondary school.