Basz began karting in 2001, competing primarily in the Polish Karting Championship and winning its K60A class in 2004. After receiving a full karting license that same year, he won the ICA-Junior class of the Polish Karting Championship in both 2005 and 2006, establishing himself as one of the country's most promising young talents.
From 2007 onward, Basz raced in Europe with increasing regularity, entering the WSK International Series alongside domestic campaigns. He joined Tony Kart and claimed victories in the 2013 International Super Cup and the 2014 WSK Champions Cup, both in the KF class. A move to Kosmic Racing Department in 2014 proved fruitful: Basz won the WSK Gold Cup and the Karting World Championship in 2015 in the KF class, then took the WSK Final Cup in 2016 in the newly rebranded OK class. He remained with Kosmic until retiring from karting in 2018.
Basz stepped up to car racing in 2017 with Antonelli Motorsport in the Super GT Cup class of the Italian GT Championship. Across a 14-race season, he scored four podiums, including a best result of second at Mugello, finishing eleventh overall in the standings.
In 2018, he joined Imperiale Racing in Lamborghini Super Trofeo Europe alongside Vito Postiglione, simultaneously entering the Lamborghini Young Driver programme. He opened his account with a race-two win at Monza, added further victories at Silverstone and Misano, and led the standings heading into the final round at Vallelunga. A retirement there left him runner-up in the championship, though he demonstrated clear pace throughout the season.
After winning Lamborghini Super Trofeo Middle East in early 2019, Basz returned to Imperiale Racing for the Super Trofeo Europe season partnering Bartosz Paziewski. The duo switched to the Pro-Am class for the final round and won the Lamborghini World Finals at Jerez, claiming the Pro-Am title.
For 2020, Basz moved to Vincenzo Sospiri Racing alongside Andrzej Lewandowski. The Polish pairing won both their races at Misano and at Nürburgring in Pro-Am, then clinched the Pro-Am title a round before the end of the season despite a retirement at Barcelona.
In 2021, Basz stayed with Vincenzo Sospiri Racing, again paired with Lewandowski. Though he finished runner-up to his teammate in the Pro-Am standings after missing the Nürburgring round, Basz partnered Mattia Michelotto at the World Finals at Misano. The pair won both races, giving Basz the 2021 Lamborghini World Finals overall title — his most prestigious victory to that point. He also made his debut in International GT Open that year for Olimp Racing alongside Marcin Jedlinski, and appeared in the GT World Challenge Europe Endurance Cup for JP Motorsport.
Basz joined Olimp Racing full-time for the 2022 International GT Open season, the team switching from Mercedes to Audi machinery. He collected three Pro-Am wins, including two overall podiums at Le Castellet and Barcelona, and took his maiden International GT Open class title. Alongside that, he raced in Lamborghini Super Trofeo Europe for Micanek Motorsport, represented Poland at the FIA Motorsport Games, and competed for Vincenzo Sospiri Racing in Italian GT and the 24 Hours of Spa.
In 2023, Basz swept both Red Bull Ring Pro-Am races with Olimp Racing and added wins at the Hungaroring and Monza, finishing runner-up in the class standings. He also returned to Lamborghini Super Trofeo Europe driving for Mičánek Motorsport alongside Broněk Formánek.
The 2024 campaign saw Basz rejoin Olimp Racing alongside Jedliński in the team's Audi R8 LMS Evo II. He took pole for the season opener at Algarve, finished third overall in race one, and won in class at Spa. Despite five additional Pro-Am podiums, he fell eight points short of class champion Marco Pulcini. He also made select appearances for Madpanda Motorsport and Eastalent Racing in the GT World Challenge Europe Endurance and Sprint Cups.
In 2025, Olimp Racing committed to the Ferrari 296 GT3 and Basz transitioned with the team. He also joined GetSpeed's Silver Cup effort in the GT World Challenge Europe Endurance Cup aboard a Mercedes-AMG GT3 Evo, finishing eighteenth in the Silver Cup standings. He scored a Pro-Am podium at Spa in GT Open and ended the season sixth in the class standings. He remained with Olimp Racing for a sixth consecutive Pro-Am campaign the following year.
Basz represents a rare dual-discipline champion, having won at the highest level of both international karting and Lamborghini one-make competition. His 2015 Karting World Championship and back-to-back Lamborghini World Finals titles in 2019 and 2021 mark him as one of the most accomplished Polish motorsport competitors of his generation. His sustained presence across Super Trofeo Europe and International GT Open, combined with forays into broader GT endurance racing, illustrates a methodical career built on consistency and class-level excellence rather than headline machinery.