Gunn's wife, Susan, is a painter. She won the inaugural Sovereign Art Prize in 2008, which included a cash award of €25,000. According to "The Daily Telegraph", before her marriage, Susan was "a beauty queen turned lingerie model" who "launched a fashion business". The couple met in Spain, where Susan had a bridal wear company, when Gunn was there on holiday. She told the "Telegraph", "When I first met Bryan, I knew nothing about football and had no idea who he was because he told me he was a joiner."