She finished tied for sixth place (with fellow Norwegian Astrid Sandvik) in the women's slalom at the 1956 Winter Olympics at Cortina d'Ampezzo. She also finished fourteenth in the giant slalom. Two years later, Bjørnbakken won the women's slalom at the 1958 World Championships in Bad Gastein. To date, she is the only Norwegian female world champion in alpine skiing. She later finished fourteenth in the slalom and 20th in the giant slalom of the 1960 Winter Olympics. In the Holmenkollen Kandahar event she won seven races between 1955 and 1959. She also took seven national championship titles between 1956 and 1959.