Although feminizations ending in 'ette' are not particularly popular now, Bernadette is a pleasant, feminine, but strong name that doesn't feel prohibitively dated. And though strongly associated with the saint who saw visions of the Virgin Mary--Saint Bernadette of Lourdes--it is now no longer strictly inhabiting the Catholic diocese.
Bernadette was much more widely used at one time than it is now. The year after Saint Bernadette was canonized, her name reached Number 252, and not long after the successful film The Song of Bernadette was released, it hit Number 188 in 1946.
Bernadette Peters is a contemporary bearer, and Minnie Driver's breakthrough film role was as Bernadette 'Benny' Hogan in Circle of Friends.