Hulse was drafted in the 3rd round (66th overall) in the 1992 NHL Entry Draft by the New Jersey Devils. In 1995, he was on the American Hockey League's Calder Cup championship team, Albany River Rats. On February 26, 1996, he was traded to the Calgary Flames with Tommy Albelin and Jocelyn Lemieux for Phil Housley and Dan Keczmer. On March 14, 2000, he was traded with a 3rd round draft pick in the 2000 NHL Entry Draft to the Nashville Predators for Sergei Krivokrasov.