Bodine was born in Chemung, New York, at the family speedrome built by his parents. He attended Alfred State College and earned an associate's degree in mechanical engineering before turning professional. After early Modified starts at Chemung and winning the prestigious Race of Champions at Pocono in 1985, he made his NASCAR Busch Series debut at Bristol in 1985, winning in just his second career start in a Rick Hendrick-backed car. He was named one of NASCAR's 50 greatest Modified drivers of all time.
In the 1986 Busch Series, Bodine ran a full-time schedule for Howard Thomas and accumulated eight pole positions, winning at Bristol and Martinsville. He narrowly lost the championship to Larry Pearson by just seven points in one of the closest title fights in series history. He totaled five Busch Series wins and 16 pole positions across his career in the series and led over 1,000 career laps.
Bodine moved to Cup racing full-time in 1988 with Bud Moore Engineering in the No. 15 Thunderbird. He recorded his only Cup victory at North Wilkesboro Speedway in 1990, driving for Kenny Bernstein's team with crew chief Larry McReynolds. The win came under some controversy when the pace car picked up the wrong car during a long caution period, effectively gifting Bodine an uncontested pit stop that sealed his lead; NASCAR acknowledged the error but let the result stand. The win was also the final Cup victory for Buick as a manufacturer, the last for the Bernstein team, and the first oval win for McReynolds. Bodine was a career-best twelfth in points that season.
His best points result came in 1992 when he finished fifteenth with 13 top-tens, also recording a career-best average starting position of 8.1. At the 1994 Brickyard 400, Bodine ran in the top-five throughout the race and finished second after tangling with his brother Geoff while battling for the lead.
After the 1995 season — in which he drove for Junior Johnson and finished twentieth in points — Johnson sold the team to Bodine and his wife Diane to form Brett Bodine Racing. The arrangement was unusual: Lowe's sponsorship money for 1996 was paid directly to Johnson to purchase the team, while Bodine operated the No. 11 out of pocket. Despite this financial structure, Bodine competed as a full owner-driver through 2003.
Sponsorship instability defined his ownership years. A $15 million three-year deal with Catalyst Communications in 1997 collapsed when Catalyst stopped paying, causing the team to plummet to 29th in the standings. Paychex provided reliable backing in 1998, allowing Bodine to qualify for every race and finish 25th. When Ralphs Supermarkets took over in 2000, a failed half-sale of the team to businessman Richard Hilton left it behind in development, and Bodine missed multiple races.
By 2001 Bodine was the last full-time owner-driver in the series — a once-common arrangement that had become economically unviable as engineering costs escalated. Teams operated by Darrell Waltrip, Ricky Rudd, Bill Elliott, and Geoff Bodine had all folded or been sold in the preceding years. Despite qualifying for every race in 2001 with Wells Fargo and RedCell as sponsors, Bodine could not attract the funding needed to remain competitive. His team was sold following the 2003 season.
Bodine also became the first Cup Series driver to wear the HANS device in race conditions, during the 2000 season.
After retiring as a driver in 2003 following 480 Cup starts, Bodine joined NASCAR's Research and Development Center as director of cost research and served as the liaison between NASCAR and teams on cost-reduction initiatives. He drove the NASCAR Car of Tomorrow prototype for testing. From 2004 to 2018 he drove the Cup Series pace car on race days. He currently serves as chairman of NASCAR's Driver Approval Committee.