Buescher was born in Melbourne, Florida, and raised in Plano, Texas. His earliest competitive success came in 2004, when he won the Young Gun division of Bandolero racing at Texas Motor Speedway. He then moved into the American Speed Association, earning the Late Model Series South championship in 2006 and the Most Popular Driver award.
In 2007, Buescher contested a partial ARCA Series schedule and became the youngest race winner in ARCA history, taking victory at USA International Speedway on his series debut. He also ran four Busch East Series races, collecting top-ten finishes in each.
Buescher signed with Braun Racing for six Nationwide Series races in 2008, debuting at Phoenix International Raceway in the No. 32 Toyota. He earned his first series top ten at Gateway International Raceway and his first career series pole at Memphis Motorsports Park.
He returned to the Nationwide Series periodically through 2010 and 2011, including stints with Phoenix Racing and Turner Motorsports. A notable result came on February 25, 2012, when Buescher won the Nationwide season opener at Daytona, coming from 11th to lead only the final lap while avoiding a massive last-lap crash. In 2014, driving the No. 99 Toyota for RAB Racing with Rheem sponsorship, he finished tenth in Nationwide Series points.
The Truck Series was Buescher's primary arena. He joined Circle Bar Racing in the No. 10 Ford for the full 2009 season, finishing 14th in points. He then moved to Turner Motorsports for 2010, collecting ten top tens in 21 races with two runner-up finishes.
In 2011 with Turner Scott Motorsports, running a full 25-race schedule, Buescher strung together thirteen consecutive top-ten finishes and battled Austin Dillon and Johnny Sauter for the championship deep into the season. A heartbreaking fuel-mileage issue at Texas — where he ran out of fuel on the backstretch while running second — ended his championship hopes, and he finished third in points.
Buescher returned to Turner Scott for 2012 as a title contender. He won four races — at Kansas, Kentucky (twice), and Chicagoland — and entered the Homestead finale with a 21-point lead over Ty Dillon. Despite struggling in the finale and finishing 13th, he clinched the 2012 NASCAR Camping World Truck Series championship by six points over Timothy Peters. Dillon, who had closed to within one point late in the race, crashed with three laps remaining. It was the first series championship for Turner Motorsports.
After finishing third in 2013 truck points, Buescher shifted to the Nationwide Series full-time in 2014. He ran a partial truck schedule for NTS Motorsports in 2015 before retiring from full-time racing.
After several years working as a real estate agent — founding The Buescher Group in Texas under the Compass Real Estate umbrella — Buescher made a one-off return to the Truck Series for Niece Motorsports at Texas in 2020. He ran the Daytona season opener for Niece in 2021, driving the No. 44 truck, but an early incident curtailed his race.
Buescher is the cousin of 2015 NASCAR Xfinity Series champion Chris Buescher, who competes full-time in the NASCAR Cup Series for RFK Racing. James is also the son-in-law of former car owner Steve Turner, whose Turner Motorsports operation he drove for during his championship-winning years.