Bielik started playing football for his hometown club, Górnik Konin before being spotted by Lech Poznań scouts in 2012, and later joining their developmental academy. He won the Polish U-17 Championships with the club in early 2014. However, in July 2014, Bielik joined Lech's archrivals, Legia Warszawa for 50,000 zł, and on 24 August, he made his Ekstraklasa debut against Korona Kielce.
On 31 January 2017, Bielik joined EFL Championship club Birmingham City on loan until the end of the 2016–17 season. He made his debut in the starting eleven for the visit to Preston North End on 14 February, and played the whole match as Birmingham lost 2–1. His next appearance was ten days later, as a substitute after centre-back Paul Robinson was sent off with Birmingham 2–0 up away to Wolverhampton Wanderers. Bielik partnered Ryan Shotton in central defence as Birmingham conceded once but, thanks in part to his "two last-ditch challenges in the closing stages", managed to hold on for the win. Playing on the right of a back three alongside Shotton and Robinson in mid-March against Newcastle United, Bielik contributed to a clean sheet, a performance that confirmed his place in the starting eleven for the next few weeks and encouraged manager Gianfranco Zola to consider loaning him again in 2017–18. Zola's dismissal coincided with the return to fitness of Michael Morrison and Birmingham's need for points, and incoming manager Harry Redknapp reverted to a back four and prioritised playing to the team's strengths for the last three matches of the season. He used Bielik only in the final match, away to Bristol City, as a substitute playing in front of the defence to help the team hold on to their one-goal lead and thus avoid relegation to League One.
A shoulder injury that required surgery prevented Bielik going out on loan in the summer 2017 transfer window, but on 31 January 2018, he signed for Walsall of League One on loan until the end of the season.
Charlton Athletic (loan)
On 16 August 2018, Bielik joined Charlton Athletic on a season-long loan. His first senior goal gave Charlton a 2–1 win against Southend United on 1 September. He scored in the League One play-off semifinals against Doncaster Rovers, and was awarded Man of the Match in the final against Sunderland, a 2-1 victory at Wembley Stadium by which Charlton Athletic secured promotion to the Championship. He played 34 games in all competitions scoring 4 goals during his spell at Charlton, playing in both centre back and defensive midfielder positions in his time at the club.
Derby County
On 2 August 2019, Bielik joined Derby County on a five-year contract. The fee was undisclosed, but reported by the Telegraph as an initial fee of below Derby's record fee paid of £8 million, plus performance-related clauses that could take it "towards the £10 million mark".
Bielik can play either as a centre back or as a defensive midfielder. He is known for his technique, passing ability and also his aerial dominance off the ball.