After starting his youth career at Herfølge, Brøndby and Copenhagen in Denmark, Bidstrup transferred to German club RB Leipzig as a 16-year-old.

The midfielder joined Brentford B from RB Leipzig in July 2020, making 14 first-team appearances during his time in TW8.

Six of those outings came during the 2020/21 Sky Bet Championship campaign, and he was on the pitch at the final whistle when the Bees won promotion to the Premier League, beating Swansea City in the play-off final.

Bidstrup made eight further appearances for the club during the 2021/22 season, including four as a substitute in the Premier League.

The 22-year-old spent the second half of the 2021/22 campaign on loan at Nordsjaelland.

He rejoined Nordsjaelland in the summer of 2022, this time on a season-long loan. He made 30 appearances for the Danish Superliga side during the 2022/23 term and won the club’s Player of the Year award.

Bidstrup joined Red Bull Salzburg for an undisclosed fee in July 2023 and has gone on to make multiple appearances in the Champions League for the Austrian side.