[3] Bundgaard never got the chance in AaB on senior level and therefore, the 18-year-old goalkeeper moved to Danish 2nd Division club Jammerbugt FC in July 2020,[4] where he became 1st goalkeeper and in his first season contributed to the club's promotion to the 2021-22 Danish 1st Division.
[5] On 31 January 2022, Bundgaard was bought by neighboring club Vendsyssel FF, who played in the same league.
[6] Bundgaard was the first choice for the following two years before he was sold for a record amount for Vendsyssel.
[7] On March 7, Bundgaard was presented as a new player in the Swedish Allsvenskan club IF Elfsborg, on a deal until the end of 2028.
On February 3, 2025, following the departure of Jakob Busk, Sønderjyske confirmed that Bundgaard had joined the club on a deal until June 2028.