Kammala jumla mai zuwa: An haifi Bourque a Boston amma ya girma a Topsfield, Massachusetts, kuma ya sauke karatu daga Kwalejin Cushing a shekara ta 2004. Yayin da yake can, ya kasance abokai na kusa da Keith Yandle. An zaba shi a matsayin na 33 a cikin
2004 NHL Entry Draft da Washington Capitals, kuma ya buga wa Portland Pirates da Hershey Bears na Ƙungiyar Hockey ta Amurka (AHL) kafin a kira shi zuwa NHL a watan Nuwamba 2007. Ya buga wasanni hudu na NHL gaba daya kafin a sake tura shi zuwa Hershey a watan Fabrairun 2008.