Bart Claessens studied trombone at the Rotterdam Conservatoire with George Wiegel, Jörgen van Rijen, Pierre Volders and Ben van Dijk. He has also had private lessons and participated in masterclasses with Joseph Alessi, Michel Becquet, Bart van Lier, Christian Lindberg and Jonas Bylund.

Claessens joined the Concertgebouworkest as a tenor and bass trombonist while still a student in March 2002, and was appointed principal trombonist of the orchestra in 2007.

He is an active member of various chamber music ensembles, such as the Ebony Band and Concertgebouworkest Brass. He also gives regular solo performances.

He teaches trombone at the Maastricht Academy of Music and gives masterclasses during Concertgebouworkest tours.