Rubuta ci gaba don wannan sakin layi - An haifi Bourque a Boston amma ya girma a Topsfield, Massachusetts, kuma ya kammala karatu daga Kwalejin Cushing a shekara ta 2004. Yayin da yake can, ya kasance abokai na kusa da Keith Yandle. An rubuta shi na 33 a cikin 2004 NHL Entry Draft
da Washington Capitals, kuma ya buga wa Portland Pirates da Hershey Bears na American Hockey League (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.