Her World Cup debut was on December 12, 1986, finishing 31st in the downhill from Val-d'Isère . She got her first World Cup points on December 4, 1987 in the same place as tenth of the downhill. One day later she caused a surprise when she unexpectedly won the second descent with the high start number 36 and taking advantage of the better conditions (source: "Salzburger Nachrichten" of December 7, 1987, page 13; headline: "Great" the show stolen). During the 1987/88 season she was classified three more times among the top 15, at the 1988 Winter Olympics she was eleventh in the downhill. The best result in the winter of 1988/89 was a third place, in the winter of 1989/90 a fourth place.
The most successful World Cup season was in the winter of 1990/91 . She won a Super-G and two downhill runs, plus five more downhill podium places. With that she won the downhill discipline ranking ahead of the Austrians Sabine Ginther and Petra Kronberger , and she finished fourth in the overall ranking. She celebrated the greatest success of her career at the 1991 World Championships in Saalbach-Hinterglemm when she became the combined world champion .
In the 1991/92 season she won a World Cup downhill run, and she was also third once. At the 1992 Winter Olympics , she just missed a medal as fourth of the combination, in the downhill and in the Super-G she was eliminated. In the 1992/93 season , Bournis won two more World Cup runs . Then, however, their level of performance sank considerably. In the 1993/94 season Bournisse did not get beyond a tenth place and missed qualification for the Olympic Games. After another solid season with a seventh place as the best result, she resigned from top-class sport in March 1995.
Switzerland
