William was the son of Glasgow Celtic legend Peter Somers. His father Peter played for Celtic for more than ten years and earned four caps for Scotland. Peter died in 1914.
Bill started his career with Coalburn Juniors F.C. in Scotland. In 1930 he joined Toronto Scottish. He was the captain of the club when they played in the Dominion Cup finals in 1931.
His brother John also started his career with Coalburn Juniors. John joined Scottish League club Heart of Midlothian in 1928. After five games and one goal for Hearts, he joined Dublin club Dolphin in the Irish Free State League.
Bill won the 1932 Dominion Cup with Toronto Scottish.
Bill was the star of Toronto Scottish when they won the 1933 North American Soccer Championship by beating St. Louis Stix, Baer & Fuller. Due to business reasons he could not play in the 1933 Dominion Cup finals in Winnipeg with Toronto Scottish.
In May 1934 Bill was forced to retire from soccer due to an injured groin muscle. The injury was sustained when the Scottish played against St. Louis Stix, Baer & Fuller in an exhibition game during Christmas 1933.