Edy Bruggmann represented Switzerland in alpine skiing’s giant slalom at the 1964 Winter Olympics and finished 19th, but he did not gain international attention until he earned a victory in the discipline at a World Cup event in January 1968. He was second in the giant slalom and 3rd and 10th in the downhill at his next two World Cup appearances, and then appeared at the 1968 Winter Olympics, where he was 10th in the downhill and 12th in the giant slalom. He earned three more podium finishes at the World Cup, including a victory in the slalom, in the lead up to the 1970 World Championships, where he was fifth in the combined. He began the 1971 World Cup season by winning a giant slalom event, and had four more podium finishes prior to the 1972 Olympic Games, where he won silver in the giant slalom ahead of his compatriot Werner Mattle. Bruggmann was also eighth in the slalom.
Bruggmann earned two additional victories in the giant slalom World Cups, within three days of one another in March 1972, prior to his retirement from active competition in early 1974. In all he had 14 podium placements in World Cup, 9 in giant slalom, 1 in downhill, and 4 in slalom. He was runner-up in the giant slalom seasonal title in 1967/68 and 1971/72, with a best finish of third in the 1971/72 overall World Cup. Bruggmann later operated a hotel and sports resort in Flumserberg.