With Brøndby, Bjur went on to win the 1996–97 Superliga and 1997–98 Superliga championships, as well as the 1998 Danish Cup trophy. He was a part of Brøndby's campaign in the 1998–99 UEFA Champions League tournament, and played a total of 54 games for Brøndby in the European competitions. After more and more games of not feeling satisfied with his own performances, he decided to end his career in November 2000, 32 years old. He went on to concentrate on his studies at the University of Copenhagen.