Born in Winthrop, Maine, Bissonette attended Kents Hill School, Westbrook Seminary, the University of New Hampshire and Georgetown University before signing a professional baseball contract with Valleyfield-Cap de la Madeleine in the Class B Eastern Canada League in 1922.
The following season, Bissonette joined the Brooklyn Robins - the once and future Dodgers - of the National League and continued his lusty hitting, batting .320