Bielser played his youth football for FC Pratteln and then moved on to FC Aesch. As senior he played for
Biel-Bienne and
Lausanne-Sport before he moved to
Basel for the first time. After two seasons he again played for Biel-Bienne before returning to Basel. Between 1952 and 1957 Bielser played 106 games for Basel and scored of 32 goals; 66 of these games were in the
Nationalliga A, 8 in the
Swiss Cup and 32 were friendly games. He scored 19 goals in the domestic league, 3 in the Cup and the other 10 during the test games. The biggest success in his football career was as Basel won the championship title in
the 1952–53 season. During this season Bielser played 21 league games and scored 9 goals for the club. Joint with
Walter Bannwart and
René Bader, Bielser was the team's second most successful league scorer with 9 goals for the club, behind
Josef Hügi with 32. ==Private life==