Bölükbaşı started motocross racing at the age of 5, and won the Turkish Championship a year later.

Making a switch back to real cars in May 2019, Bölükbaşı started racing in the GT4 European Series, and made his open-wheeler debut in October the same year in Formula Renault Eurocup.

Bölükbaşı left Charouz Racing System before the Spa-Francorchamps Formula 2 round on 27 August 2022.

[5] In late 2017, he was selected to join G2 Esports FA Racing, in which he would compete in various simracing competitions throughout 2018.

In the 2018 Formula One eSports Series, he switched to Toro Rosso and participated in 4 out of the 10 races, finishing 12th with 32 points.

During the 2020 lockdowns, Bölükbaşı competed in several virtual races,[7] including winning the inaugural championship of the Formula Renault Esport Series.

[14] In January 2021, BlackArts Racing announced that Bölükbaşı would drive for the team in the 2021 F3 Asian Championship.

[22] In early February, just before round 3, Bölükbaşı announced that he would not continue racing in the series, as his chances of getting FIA Super Licence points were slim.

[23] On 3 July 2021, it was announced that Bölükbaşı would join the 2021 Euroformula Open Championship with Van Amersfoort Racing.

[29] Bölükbaşı started race 3 in 7th, but collided with teammate Rafael Villagómez, causing both of them to retire.

[38] Bölükbaşı was signed by Evans GP to contest the first round of the 2022 Formula Regional Asian Championship.

[42] He drove a Formula 2 car for the first time in an official session during the 2021 post-season test with Van Amersfoort Racing on 18 December 2021, finishing 22nd and last.

[43] On 12 January 2022, it was officially announced that he would compete in the 2022 Formula 2 Championship as a Charouz Racing System driver.

He later overtook two more cars and finished in 14th, also ahead of Marcus Armstrong and Theo Pourchaire, both of whom retired from the race.

Following a late-race crash, Bölükbaşı made a pitstop under the safety car, and two other drivers having issues in the pitlane helped him to get back up into 12th.

[51] During the first day of the in-season Formula 2 test in Circuit de Barcelona, Bölükbaşı crashed into a concrete wall.

He missed the rest of testing and flew back to Turkey,[52] where it was revealed that he had a broken rib.

He came into the pits after the safety car for a tyre change but had a slow pitstop, finishing the race in 20th place.

[60] He was due to start in 20th in the feature race, but Roy Nissany and Liam Lawson stalling on the grid on the formation lap promoted him to 18th.

On lap 12, while running in 16th place, he was tapped by Roy Nissany, and collided with the barriers, causing both drivers to retire.

[73] In the feature race, he made contact with Liam Lawson, causing him to break his front wing and pit early.

[82] Bölükbaşı's contract was terminated by mutual consent ahead of the Spa-Francorchamps round, and he was replaced with Tatiana Calderón.

[83] On his sudden F2 departure, Bölükbaşı stated that financial issues forced him to part ways with Charouz.

[85] In March 2023, Bölükbaşı was chosen to compete in the 2023 Super Formula Championship with TGM Grand Prix.

[88] After leaving Super Formula, Bölükbaşı found a drive to race in the 2024 European Le Mans Series for DKR Engineering.