Bourque was born in Boston but grew up in Topsfield, Massachusetts, and graduated from Cushing Academy in 2004. While there, he was close friends with Keith Yandle. He was drafted 33rd overall in the 2004 NHL Entry Draft by the Washington Capitals, and played for the Portland Pirates and Hershey Bears of the American Hockey League (AHL) before being called up to the NHL in November 2007. He played four NHL games total before being reassigned to Hershey in February 2008.