Bouchard began racing at Brookline Speedway in 1963 as a substitute driver for his father's car. After high school, he moved up to late models at Seekonk Speedway and claimed five consecutive track championships from 1967 to 1971. Car owner Bob Johnson noticed Bouchard's talent and placed him in a modified at Stafford Speedway, where he won his first of 35 career victories at the track in April 1972. Bouchard went on to win the 1973 and 1979 Stafford modified championships, and also competed successfully at Thompson Speedway, Seekonk Speedway, Waterford Speedbowl, and Westboro Speedway.
He was a notable rival of fellow New Englander Geoff Bodine, and the two battled repeatedly for modified wins. Bodine later recommended Bouchard when Hendrick Motorsports launched its Busch Series program in 1984, leading to a one-race opportunity with the team.
Bouchard entered the 1981 NASCAR Winston Cup Series in the No. 47 Jim Stacy Buick, owned by Jack Beebe's Race Hill Farm team. Racing only 22 of 31 scheduled events, he still earned the Rookie of the Year title through consistency — posting twelve top-ten finishes and one landmark victory.
That victory came at the Talladega 500. Running third behind Darrell Waltrip and Terry Labonte on the final lap as the two leaders traded paint side by side out of the last turn, Bouchard found an opening beneath them both and nosed ahead at the line in a photo finish. Waltrip, who had been focused on Labonte and never saw Bouchard coming, famously asked afterward: "Where the hell did he come from?" Waltrip later admitted he had not tried to block Bouchard because he assumed the newcomer was a lap down. The win is widely regarded as one of the biggest upsets in NASCAR history.
In 1982, Bouchard had a career-high eighth-place points finish with fifteen top-tens in thirty races. He ran full-time in 1983, 1984, and 1985, finishing between eleventh and sixteenth in the standings each year. Near-wins at Martinsville in 1984, where Bodine edged him to settle the old rivalry, and at Rockingham in 1985, where Waltrip passed him late, highlighted the competitiveness of a team that rarely had the resources of the front runners.
Bouchard switched to the No. 98 Valvoline Pontiac for Mike Curb's Curb Agajanian Performance Group in 1986, then drove five events for Hoss Ellington in 1987 before stepping away from Cup racing.
Bouchard was inducted into the New England Auto Racers Hall of Fame in 1998 as part of its inaugural class. After his driving career, he returned to Fitchburg and built Ron Bouchard's Auto Stores into a prominent regional dealership representing Honda, Acura, Stellantis, Kia, and Nissan. In September 2015, three months before his death from cancer, he opened a museum at his Stellantis dealership celebrating his motorsport history. Since 2016, the New England Auto Racers Hall of Fame has awarded the Ron Bouchard Award for lifetime service to motorsport in the region.
His brother Ken Bouchard won the 1988 NASCAR Winston Cup Rookie of the Year award, making the Bouchards one of only a handful of sibling pairs to each claim the honor.