He played junior hockey for the Kitchener Rangers and the Ottawa 67's from 1972 to 1975. The St. Louis Blues chose him 63rd overall in the 1975 NHL Amateur Draft while the Michigan Stags picked him 48th overall in the 1975 WHA Amateur Draft.
In his first three years of pro hockey Bouronnais played in 71 games for the Blues (scoring 9 goals and 15 assists) but was not able to crack their lineup as a regular. In 1981 he went to Europe where he played for 11 years.
He retired in 1992.