Bridewell grew up in Wiltshire and began motorcycle racing as a teenager. An early highlight came when he finished runner-up in the Yamaha R6 Cup in 2005. He progressed into British Superbikes alongside his older brother Ollie, and for the 2007 season the two brothers joined team NB Suzuki together.
The 2007 season was cut short by tragedy. Ollie Bridewell died following a crash during a practice session at the Mallory Park round of the British Superbike Championship. He was pronounced dead at the scene. Tommy left the championship immediately after that round, and the loss of his brother cast a long shadow over his subsequent career.
Bridewell restarted his racing career in Italy during 2008 and attempted the European Superstock 600 class in 2009, riding for the Lorenzini Yamaha team. His campaign produced only a 13th-place finish in the opening round at Valencia before he departed the team mid-season. He returned to British Superbikes during the 2009 season, competing in the Privateers' Cup on a Team NB Suzuki and winning the Cup class in seven of the 26 races.
The results earned him a full-season British Superbike contract with Quay Garage Honda for 2010, where he posted a career-best fourth-place finish at Cadwell Park and ended the season 11th overall. In 2011, he sustained a further setback when a heavy crash in practice at Thruxton led to the amputation of his little finger. He was released by the Tyco Honda team mid-season and moved to Motorpoint Yamaha for the final four rounds.
Bridewell spent seasons with Shaun Muir Racing in 2013 and 2014, then joined Tyco BMW in 2015. From 2018 onward he aligned with Oxford Products-backed teams on Ducati machinery. During the 2018 season his contract with a Suzuki team was terminated abruptly in practice at Snetterton, but he recovered to join Moto Rapido Racing on a Ducati Panigale, filling the seat vacated by Taylor Mackenzie. He claimed four podium finishes for the remainder of that season, narrowly missing the Showdown but winning the Riders' Cup at the season finale.
Retained by the same team through 2019 to 2022 under updated sponsorship, his best championship result during this period came in 2021, when he finished second overall behind winner Tarran Mackenzie.
For 2023, Bridewell switched from Oxford Products to Paul Bird Racing on a factory-supported Ducati Panigale V4 R. The move proved decisive: he claimed the British Superbike Championship, delivering the title that years of near-misses had promised. The 2023 title came 16 years after his career had been interrupted by his brother's death at Mallory Park.
Bridewell made a World Superbike Championship appearance in May 2019 as a stand-in for injured Eugene Laverty on the Go Eleven Ducati at Imola, Italy. He scored four World Championship points with a 12th-place finish in Race 1 and added further points in a subsequent appearance at Jerez later that season. In 2024, he entered the final world championship round at Jerez as a wildcard on his BSB-specification Honda Fireblade.
Bridewell contested the 2018 Suzuka 8 Hours endurance race, competing for Japanese team S-Pulse Dream Racing IAI on a Suzuki GSX-R1000R. Racing alongside two teammates, the squad finished fourth overall — a strong result in one of motorcycle endurance racing's most demanding events.
Following his 2023 championship victory, Bridewell confirmed a move to Honda Racing UK for 2024, joining a factory-supported team based in Louth, Lincolnshire, alongside Andrew Irwin and Dean Harrison. The team ran Honda Fireblade machinery.
Bridewell's championship win in 2023 closed a long chapter of promise and adversity. Racing in memory of a brother lost on the same circuits where he later competed, he represents one of British motorcycle racing's more resilient careers — built from repeated setbacks into eventual success at the highest domestic level.