Born in Toronto and raised in Guelph, Ontario, Asselstine's NHL officiating career started in 1979 and ended in 1997. During his career (in which he wore a helmet from the mid-1980s until his retirement), he officiated 1,364 regular season games and three All-Star games. An imposing man, Asselstine's nickname on the ice was "Bear". This nickname was given to him for his no-nonsense attitude in policing fights, and his impressively hairy 6-foot-2, 225 lb body.
On January 28, 1989, at the Boston Garden, Asselstine was made famous when a fan came onto the ice during a hockey game and Asselstine bumped him right into the boards. The fan was then taken into custody.
Asselstine was honoured in 2007 with the Caring Canadian Award for his work as founder of the Guelph Wish Fund for Children (begun in 1984). His award was presented by Governor General Michaëlle Jean.