[3] Bidstrup was a part of the RB Leipzig U19 team which reached the 2019 DFB-Pokal Junior Final and despite having three years remaining on his contract,[4][5] he departed the club in July 2020.

[6] On 16 July 2020, Bidstrup joined the B team at English Championship club Brentford on a three-year contract, with the option of a further year,[6] for an undisclosed fee.

[13] Bidstrup made six late-season appearances, including a substitute cameo in the promotion-clinching 2–0 2021 Championship play-off final victory over Swansea City on 29 May.

[16][17] Three weeks later and in need of "a run of consecutive matches in order to progress to the next level", Bidstrup joined Danish Superliga club Nordsjælland on loan until the end of the 2021–22 season.

[21] On 16 July 2023,[22] Bidstrup transferred to Austrian Bundesliga club Red Bull Salzburg and signed a five-year contract for an undisclosed fee.

[27] Bidstrup won his maiden call-up to the senior team for a pair of Nations League fixtures in October 2024 and he remained an unused substitute in both matches.