There is air service to Bora Bora but aside from corporate jets, it's all inter-island prop planes. Bora Bora is about at 40 minute flight from Tahiti and it is a very scenic flight as long as you are on the correct side of the plane. (I can't remember offhand which side that is right now).

The airline that provides service to Bora Bora is Air Tahiti (as opposed to Air Tahiti NUI -- "Nui" I believe means "far"). If you look on the web, you should find Air Tahiti's website.