Bodine's father and grandfather built Chemung Speedrome the year after his birth, and he began racing in the micro-midget division there at age five. By the time he arrived in NASCAR's premier division in 1979, he was already a dominant figure in Northeast Modifieds, holding championships at Stafford Speedway, Shangri-La Speedway, Spencer Speedway, and Utica-Rome Speedway. He won major Modified events including the Race of Champions, the Oxford 250 (1980, 1981), the Oswego Classic (1981), and the Lancaster 200 (1978, 1981). His 1978 season stands as one of the most statistically dominant single seasons in Modified history: driving cars owned by Dick Armstrong, Bodine started 84 feature events and won 55 of them, a figure recognized in the Guinness Book of World Records as the most wins in one season in any form of motorsport.
Bodine made his first full Winston Cup season in 1982 and won the Rookie of the Year award. His first Cup victory came in 1984 at Martinsville — also the first win in the history of Hendrick Motorsports, the team he drove for at the time. He recorded his most prestigious win at the 1986 Daytona 500, NASCAR's flagship event. Other significant victories included the 1992 Busch Clash, the 1994 Winston Select, and a final Cup win at Watkins Glen in August 1996, where he beat Terry Labonte to the line by 0.44 seconds.
Bodine won the 1987 International Race of Champions championship and earned the 1994 Busch Pole Award for the most poles in a season. His best season points finish was third in 1990. In 565 Winston Cup starts he recorded 18 wins, 37 poles, and more than $16 million in career winnings. He was named one of NASCAR's 50 Greatest Drivers during the series' 50th anniversary.
Bodine drove for Hendrick Motorsports, Junior Johnson, Bud Moore, and operated his own team after purchasing the assets of Alan Kulwicki's race team following Kulwicki's death in April 1993. He was also the last driver to win a race and lap the entire field, accomplishing this at North Wilkesboro Speedway in the fall 1994 race. He holds the all-time qualifying record at Atlanta Motor Speedway from a polesitting run following the track's 1997 repave, clocking over 197 mph.
Bodine introduced power steering and full-face helmets to Winston Cup competition.
A heated rivalry with Dale Earnhardt defined much of Bodine's late 1980s career. An incident at the 1987 Winston — where Earnhardt knocked Bodine and Bill Elliott out of his way to win — escalated through a series of retaliatory incidents in Busch Series and Cup races over the following year, with NASCAR levying fines and penalties on both sides before a formal resolution was reached at a Daytona Beach meeting in 1988. Bodine later said the two had been close friends before NASCAR and that competitive pressures changed their relationship.
On February 18, 2000, Bodine was involved in one of the most violent crashes in NASCAR Truck Series history during the inaugural Daytona 250. On lap 57, contact between several trucks in the tri-oval caused Bodine's No. 15 Ford to vault over the outside retaining wall and into the catch fencing nose-first at nearly 190 mph. The truck's fuel cell ruptured, the front of the vehicle was destroyed, and it rolled nine times before coming to rest on its roof. Thirteen trucks were involved; nine spectators were also injured. Bodine suffered fractures to his right wrist, right cheekbone, a vertebra in his back, and his right ankle, plus a concussion. He returned to Cup racing just ten races later at Richmond.
Inspired by watching the 1992 Winter Olympics, Bodine co-founded Bo-Dyn Bobsleds with chassis builder Bob Cuneo of Chassis Dynamics in 1992 — the name combining "Bodine" and "Dyn" for Chassis Dynamics. The project applied NASCAR engineering methods to bobsled construction for the U.S. national team. The U.S. team first used Bo-Dyn sleds in 1994; in 2002 they won three medals at the Salt Lake City Winter Olympics using the sleds, and in 2010 pilot Steven Holcomb drove a Bo-Dyn sled named "Night Train" to gold at the Vancouver Winter Olympics.
Bodine announced his retirement in October 2012 after 27 seasons in NASCAR. He subsequently worked as a Driver Analyst and opened a Honda Power Sports dealership in West Melbourne, Florida.