At the beginning of his career, Bieler was a downhill specialist . In the 1973/74 season of the European Cup , he took third place in the downhill classification. He scored his first points in a World Cup race on February 3, 1973 as tenth on the downhill run from St. Anton am Arlberg . A week later, Bieler improved to fifth place in the same discipline in St. Moritz . In the following two winters, however, he could never classify himself in the points, which is why he gradually turned to the technical disciplines.
In the World Cup season 1975/76 Bieler was back to success. Eight times he drove into the top ten, where he celebrated his only victory on January 18, 1976 at the giant slalom in Morzine . At the 1976 Winter Olympics , he finished eighth in the giant slalom, while in the slalom he was eliminated after fourth-fastest time in the first run.
The 1976/77 season was similarly successful . Bieler was among the top ten in eleven World Cup races, including a second and a third place in the slalom. In addition, he won the Italian slalom championship. In contrast, Bieler did not come in ninth place in the 1977/78 season , which is why he resigned from top-class sport at the end of winter.