Boucha was selected by the Detroit Red Wings in the second round of the 1971 NHL Amateur Draft and went on to make his NHL debut that season. Along with the Red Wings, he also suited up for the Minnesota North Stars, Kansas City Scouts and Colorado Rockies, before retiring in the 1976-77 season.
During a game in January 1975, Boucha was attacked by Boston Bruins forward Dave Forbes which left him with a cracked bone around his eye and blurred vision, which affected the remainder of his hockey career as he never fully recovered.
In 247 games with the Red Wings, North Stars, Scouts and Rockies, Boucha had 102 points (53 goals, 49 assists), 157 penalty minutes and was a minus-53.