Bursik began his career at the youth academy at AFC Wimbledon, where he spent eight years before joining Stoke City on 1 July 2017.
[9] Bursik played 20 matches for Stanley in 2019–20 until the season was ended early due to the COVID-19 pandemic at the time Accrington were in 17th position.
[14] Bursik joined Peterborough United on 8 April 2021 in an emergency loan deal following a season ending injury to Christy Pym.
[16] On 18 May 2021 Bursik joined Lincoln City on an emergency loan for their League One play-offs following a head injury to Alex Palmer.
[23] Bursik was the starting goalkeeper for the England Under-17 team that lost to Spain on a penalty shoot-out in the final of the 2017 UEFA European Under-17 Championship.