I suppose Shamus that if you say to her 'You look for a bi woman if you want, I will look for who I want' than the stigma of UH is taken off of you, you need not look for a partner you both 'share'. If this is her desire, leave her to it and make it clear that you are happy to be friendly and respectful to anyone she meets but you don't want to feel obligated to partner up with them too.
Sorted!
