If there was one thing Bill Burega could do, is was intimidate the opposition. An imposing figure, he liked to play a rough and tumble style of game. In 1952-53, he played 72 games with the Glace Bay Miners, scoring 16 points while sitting 163 minutes in the penalty box. In 1953-54, Burega played for three teams; the Pittsburgh Hornets and the Ottawa Senators and Quebec Aces of the QHL. It was in 1955-56, when as a member of the WHL's Winnipeg Warriors, Burega received a call to play as a fill-in for the Toronto Maple Leafs where he had one assist in four games, which were his final NHL totals. He also helped the Warriors to the WHL championship that year, while leading the playoffs with 33 minutes in penalties.
Burega played another nine years as a pro with eight different teams. The one constant was his willingness to mix it up. He spent at least 100 minutes in the penalty box during ten of his 13 professional seasons.
Among some of Burega's accomplishments included; playing for the 1955 Calder Cup winning Pittsburgh Hornets, while also leading the playoffs with 24 penalty minutes in ten games, and playing for the WHL champion Winnipeg Warriors in 1956.