With increasing his production in each of his first two full WHL seasons, Bourke as a then diminutive sized forward was selected 72nd overall in the 2012 NHL Entry Draft by the Colorado Avalanche.

Bourke was then signed to an amateur try-out contract with the Avalanche's AHL affiliate, the Lake Erie Monsters on March 19, 2014.

[3] Upon attending Colorado's NHL training camp, Bourke was reassigned to Lake Erie to begin his first full professional season in 2014–15.

[7] Following two productive seasons in the DEL, Bourke left Germany as a free agent and was signed to a one-year contract with Finnish club, Oulun Kärpät of the Liiga, on May 28, 2021.

On June 3, 2022, Bourke left Finland as a free agent and continued his European career by signing a one-year contract with Austrian-based, EC Red Bull Salzburg of the ICEHL.