Beebe made his NASCAR debut in 1989 in the premier Winston Cup Series, running a single race at Sonoma in a car owned by his father. He qualified the No. 93 Taco Bell Buick 32nd and completed nearly the full race distance, finishing 24th.
In 1990, Beebe made four Winston Cup starts, splitting time between his family-owned car and machinery owned by D.K. Ulrich. His results did not match his 1989 debut, with a best finish of 30th at Sonoma. His strongest qualifying effort of those four races came at Michigan, where he started 28th.
Beebe committed his team to the NASCAR Busch Series beginning in 1991, running 23 races in the No. 9 Taco Bell car. He debuted that season at Richmond, qualifying 31st and finishing 24th. At the following race at Martinsville he improved to eleventh place, and a qualifying effort of fourth at Hickory represented one of his best starts of the campaign. Beebe grew stronger through the second half of the year, recording eleven top-twenty finishes and capping the season with his first career top-ten — a tenth place at IRP. He ended the season 22nd in championship points.
The 1992 season was more difficult. Running only fourteen starts in the No. 24 Banana Boat Ford, Beebe suffered seven DNFs, meaning he failed to finish half his races. His best result was a fifteenth at Daytona, with only two other top-twenty finishes across the season.
Eight starts in 1993 brought similarly sparse results, with a best finish of seventeenth at Orange County and five races ending early. Beebe attempted only one Busch race in 1994, starting 39th at Dover before finishing 32nd following an engine change. His final Busch appearances came in 1995, when he ran at Darlington and Rockingham — crashing out of both events.
After stepping back from the Busch Series, Beebe entered the inaugural season of the NASCAR Craftsman Truck Series in 1995. He ran at Phoenix in the No. 10 Chevrolet, starting 24th and finishing thirtieth. He made four additional starts that year in the No. 89 Chevrolet, recording a best finish of twelfth at Saugus, where he also set his best career qualifying position of thirteenth.
Beebe's final appearance in any NASCAR series came in 1997, driving the No. 06 Farris Racing Chevrolet at Las Vegas. He qualified 24th but lasted only two laps before retiring in 39th place.
Beebe competed across all three tiers of NASCAR competition during the late 1980s and 1990s, primarily as an independent operator running family-owned equipment. His most productive season was 1991, when he established himself as a consistent Busch Series competitor before a combination of mechanical failures and limited resources curtailed further progress.