On the death of his brother, Alexander (Sandy) Hay Seton (1904-1963) who had no male heirs, Bruce inherited the former's Seton Baronetcy. He married second wife actor Antoinette Cellier (Florence Antoinette Glossop Cellier) in 1940 in London. His address at this time was 15 Learmonth Gardens, Edinburgh. They had a daughter Lydia Antoinette Gordon Seton, born on 14 November 1941. Since he had no male heirs on his death in 1969, the title passed to his cousin, Christopher Bruce Seton (1909–1988).