Bliss began racing at the age of ten and worked his way through amateur and regional competition before capturing his first major title in 1993 with the USAC Silver Crown National Championship. He entered the NASCAR Craftsman Truck Series in 1995, driving for Ultra Motorsports, and immediately showed promise by winning at North Wilkesboro Speedway in his debut season of nineteen races. Over the following seasons with Team ASE Racing and later Roush Racing, Bliss accumulated multiple wins and consistent top-ten finishes in the Truck Series while also beginning to make occasional appearances in the NASCAR Busch Series and Winston Cup Series.
After spending 2001 searching for a full-time ride, Bliss joined IWX Racing's Steve Coulter in 2002 and delivered one of his most dominant seasons. He claimed five wins and secured the Craftsman Truck Series championship, establishing himself as one of the premier talents in the division. The title earned him a move to Joe Gibbs Racing in the Busch Series for 2003, where he posted fourteen top-tens and finished tenth in points. During the same 2003 season he won at Chicagoland Speedway in the International Race of Champions. In 2004, driving for Gibbs in the Busch Series, Bliss scored his first career win in that series at Lowe's Motor Speedway and finished fifth in the championship standings.
Bliss made his Winston Cup Series debut in 1998 and attempted to break through as a full-time Cup competitor on multiple occasions. His career-best Cup finish came in the 2004 Chevy Rock and Roll 400 at Richmond, where he drove a Joe Gibbs Racing entry to a fourth-place result despite a pit-road speeding penalty, executing a late-race charge through the field. He joined Haas CNC Racing for 2005, where he narrowly missed a Cup victory in the Nextel Open when Brian Vickers made contact with him on the final lap in the final turn, pushing Vickers to the win. Bliss was visibly upset in post-race interviews, saying he would not have wrecked Vickers to take the victory.
He subsequently bounced between several organizations including BAM Racing, Phoenix Racing, Tommy Baldwin Racing, and TriStar Motorsports in both Cup and Nationwide Series competition through the early 2010s. His most consistent stretch in the Nationwide Series came with TriStar, where he posted a twelfth-place points finish in 2011 and an eighth in 2012. He also secured a second career Nationwide win at Lowe's Motor Speedway in 2009, capitalizing on fuel strategy during a rain-shortened race.
Bliss made periodic starts across the Xfinity and Truck Series through 2016 for various teams including TriStar Motorsports, Contreras Motorsports, and MB Motorsports, but never regained a consistent full-time ride. After stepping back from competition, he transitioned into a mentoring and coaching role, serving as a driving coach for Joe Graf Jr. in the ARCA Menards Series East in 2019.
A journeyman competitor throughout most of his Cup Series tenure, Bliss carved out his most lasting legacy as a Truck Series champion and a reliable, versatile presence across NASCAR's three national touring divisions. His 2002 championship remains the signature achievement of a career defined by persistence and adaptability across multiple series and team environments.