Somerville won his first American championship in 1965, qualifying his team for the 1965 Scotch Cup, the World Curling championships at the time. His team won the event, defeating Canada's Terry Braunstein in the final, making Somerville the first skip from outside of Canada to win a World championship.
In 1968, Somerville won his second U.S. championship. At the 1968 Air Canada Silver Broom (the world championship), Somerville won the bronze medal after losing to Canada's Ron Northcott, 12-2 in the semi-final. The following year, Somerville won his third U.S. championship, and at the 1969 Air Canada Silver Broom, he lost once again to Canada's Northcott, this time in the final, 9-6.
Somerville also played in the 1988 and 1992 Winter Olympics, when curling was a demonstration sport. He finished fourth place in 1988, and won a bronze medal in 1992. 1995 would mark his last World Championship appearance, when he was alternate for his son Tim's team.
Bud's son, Tim is also an American champion, having won the U.S. nationals 1995, 1996 and 1999.
Somerville was the first inductee to the United States Curling Hall of Fame in 1984.