Her participation in the 1984 Helsinki Ballet Competition netted Toussaint first prize for his choreography in Un simple moment.
She danced the role of Giselle for the first time in Odessa, Ukraine, USSR, in 1988.
She has also performed in some 10 ballets by George Balanchine.
Throughout her career with Les Grands, Bissonnette has worked with such choreographers as James Kudelka, William Forsythe, Jiri Kylian, Ohad Naharin, Nacho Duato, Nils Christe, Susan Toumine and Hans van Manen.
In 1995, she was made an Officer of the Order of Canada.
In 1996, she was made a Knight of the National Order of Quebec.
In 2014, Bissonnette received the Governor General's Performing Arts Award (GGPAA) for Lifetime Artistic Achievement, Canada's highest honour in the performing arts.