Bowey, a defenseman born in Winnipeg, was taken by the Washington Capitals in the second round (No. 53) of the 2013 NHL Draft after helping Canada win gold medals at the 2012 Ivan Hlinka Memorial Tournament and the 2013 IIHF World Under-18 Championship. He finished 2012-13, his second season with Kelowna of the Western Hockey League, with 30 points (12 goals, 18 assists) in 69 games.
The Capitals signed Bowey to a three-year, entry-level contract on April 2, 2014, after a 21-goal, 60-point season with Kelowna. He had 17 goals and 60 points in 58 games for Kelowna in 2014-15, and also helped Canada win gold at the 2015 IIHF World Junior championship.