Rosmarie Bleuer made her début at the junior Swiss national championships in 1945, when she took gold in the downhill and came in second in the slalom. The following year, she was junior national champion in both events and, two years later, made her senior international début at the 1948 St. Moritz Olympics. There, she finished sixth in the combined, ninth in the downhill, and thirteenth in the slalom. Her next major stop was the 1950 World Championships, where she was 15th in the downhill, 17th in the giant slalom, and disqualified in the slalom. She came in second in the slalom at the national championships in 1951, behind Olivia Ausoni, but retired from active competition at the end of the season.