Bidstrup moved from
HB Køge at the age of 12 to join
Copenhagen. He spent more than seven years in the club's
youth academy, making eight appearances during the youth team's
2023–24 UEFA Youth League campaign, During Copenhagen's
2024–25 season, he made three match-day squad lists for the first team, though he was an unused substitution in each of those occasions. He agreed with the club to a contract through to the summer of 2029, which included a clause in which Copenhagen may match future transfer offers. He made his debut for the club on 2 March, coming on as a substitute in a 3–1 league victory over
Vejle. During the team's
2025–26 season, he was moved to
left-back as teammate
Jean-Manuel Mbom frequently played as right-back. On 1 March 2026, he scored his first goal for Viborg in a 2–1 win over
FC Nordsjælland. His goal was the match winner, and secured Viborg a place in the
2025–26 Danish Superliga Championship round. ==International career==