Bleekemolen made his first Formula One attempt in 1977 at the Dutch Grand Prix, entering with a March 761 fitted with a Ford Cosworth DFV engine but failing to qualify for the race.
In 1978 he drove the ATS HS1 for the ATS team across four championship events. He failed to qualify at the Dutch Grand Prix, the Italian Grand Prix, and the Canadian Grand Prix. At the United States Grand Prix East at Watkins Glen he qualified 25th on the grid and started the race — his only Formula One championship start. He retired after 43 laps with an oil leak and was classified as a non-finisher. He scored no championship points.
Following his Formula One period, Bleekemolen contested the 1978 European Formula Two Championship with Fred Opert Racing, driving a Chevron B42 with a Hart engine.
Bleekemolen returned to Formula Three for three further seasons after the Formula One and Formula Two campaigns. During this period he won two rounds of the European Formula Three Championship and finished second in the overall standings. The driver who took the championship ahead of him was Alain Prost, who subsequently won four Formula One World Championships. The runner-up finish behind Prost in the European F3 standings is the most frequently cited result of Bleekemolen's early career.
Bleekemolen competed in the Porsche Supercup across multiple seasons through his own Team Bleekemolen operation. Recorded championship standings include: tenth in 2003 with 68 points, an entry in 2004, 13th in 2006 with 48 points, 33rd in 2007 for Bleekemolen Race Planet, and 29th in 2008 under Racing Team Jetstream.
Bleekemolen began competing in the NASCAR Whelen Euro Series in 2019, driving in the EuroNASCAR 2 class for Team Bleekemolen in a Ford numbered 69 and 70. He finished 12th in the championship with 371 points. He competed in EuroNASCAR 2 in subsequent seasons: 26th in 2021, 20th with 228 points in 2022, 12th with 305 points in 2023, and 12th with 392 points in 2024 for Racing Planet Team Bleekemolen.
In 2025 Bleekemolen stepped up to the top-level EuroNASCAR PRO class with Race Planet Team Bleekemolen, driving a Toyota numbered 72 and finishing 33rd with 56 points. He also entered the EuroNASCAR OPEN class the same year with Rette Jones Racing in a Ford numbered 30. He remained active in 2026, competing at Paul Ricard and finishing 18th.
Across his recorded career Bleekemolen has accumulated 473 race starts, 22 race victories, 88 podium finishes, and 9 pole positions.
Both of Bleekemolen's sons have become professional racing drivers. Jeroen Bleekemolen and Sebastiaan Bleekemolen have competed in GT endurance racing, international series, and various categories across Europe and North America. The Bleekemolen name has appeared continuously on race entries across multiple generations, with Team Bleekemolen and Racing Planet Team Bleekemolen serving as the family's primary competitive operations.