Bech played his youth years for Ålholm IF, Skjold Birkerød, B 1903, Lyngby BK and KB.

At Malmö, he looked to replace Swedish international striker Markus Rosenberg before the UEFA Champions League qualification, but Bech never got a breakthrough at the club.

Following one year at Malmö, he moved back to Denmark to play for Esbjerg fB in the summer 2006.

In the first half of the 2006–07 Superliga season, Bech rediscovered his goal scoring form, and was at a time the joint top goalscorer of the league.

On 15 November 2006 he got his Danish national team debut in a friendly match against the Czech Republic, when he came on the pitch in the second half, as a substitute for Peter Løvenkrands.