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.

Hulse signed as a free agent with the Phoenix Coyotes on July 10, 2003. On October 8, 2005, he was traded with Michael Rupp and Jason Chimera to the Columbus Blue Jackets for Geoff Sanderson and Tim Jackman.

On February 28, 2006, he was traded to the Flames for Cam Severson. Hulse was invited to the Carolina Hurricanes' 2006 training camp as a depth fill-in, but was cut before the season started.

Hulse married actress Gena Lee Nolin on September 3, 2004, at the Royal Palms Resort and Spa in Phoenix, Arizona. Their son, Hudson Lee Hulse, was born on April 15, 2006, in Scottsdale, Arizona. On December 3, 2008, Hulse and Nolin had their second child, a girl named Stella Monroe. Hulse has a daughter, Caia, from a previous relationship. Hulse is also uncle to Braden Hulse, born November 11, 1994.