Bassett is the daughter of John F. Bassett, who was an executive for his father John Bassett's company Baton Broadcasting, and Susan Carling, the granddaughter of politician and brewery executive John Carling.
In 1983, Bassett advanced to the quarter-finals of the Australian Open and won her first top-level singles titles in Pennsylvania. In 1984, she reached the quarter-finals at the French Open and the semi-finals at the US Open. She reached the French Open quarter-finals again in 1986. Bassett won her second top-level singles title in 1987 at Strasbourg.
Bassett named the WTA's Most Impressive Newcomer in 1983, and Canada's Female Athlete of the Year in 1983 and 1985. During her career, Bassett won a total of two top-level singles titles and two doubles titles.
Bassett married the American tennis player Robert Seguso in 1987. The couple have a son named Holden John Seguso, who was born in March 14, 1988. They have another son, Ridley Jack (1993) and a daughter Carling Jr. (1990). She currently operates a tennis academy with her husband, and Chris Evert.
On Monday, August 13th, 2007, during the Canadian Open Tennis Championships at the Rexall Centre in Toronto, Bassett, along with John McEnroe, was inducted into the Canadian Tennis Hall of Fame. After the ceremony, Bassett teamed up with US tennis great Jim Courier, for a friendly doubles match against John McEnroe and Anna Kournikova.