Oh well, it was ages back that I read those comics. If Bette was already at West Point when she asks about the Gotham Knights that Kate would say no makes sense - since she was already enrolled in training.
I find it far more likely that the real 'encouragement' for her going to West Point would have been via Jacob, not Kate though.
I still say the real reason, to be meta, is that the writers just didn't want to use Bette because she wasn't one of their favourites.