I have a cat who does this and it can be quite hard to take. Some cats seem to get over-affectionate and then don't know where to go with it, so bite, right in the middle of their purring and nudging. Mine's five and he's never got any better, despite being sprayed regularly with a water spray or being removed from the room.
So you probably have to learn to put up with this. Make sure it's not because you are restraining her whilst trying to cuddle. Always let her come to you. Don't hang on to her if she wants to be set down.
I walk around the house with my 'weapon' and I have to use it frequently. I've just had to accept that this is behavioural and deal with it. It's very wrong if your shelter didn't flag this up, but can I urge you not to give up on your kitty. It might be that she's been rejected before and really, this isn't a nasty act on her part. It's just that some kitties' personalities are a bit odd, just like some people's.