Lifeisquick-
By pushing her gently to engage in more conversation, you will not only be helping yourself, but you will be helping her. You don't need therapist for that - if she find it hard even to talk with you, then you are the ideal person to start with.
You could make it into a game. 1/4 of an hour 3 times a week for instance. Give her a list of topics that while not to challenging, she will at least find interesting. Then she must pick one topic from the list, and start a conversation with you.
If you tell her this was the one and only reason why you were worried about the relationship, she would probably be inclined to try it.
If you are thinking of leaving her anyway, I would not take no for an answer... But I am not a very nice guy
Just remember, she sounds like a beautiful being with the most sensitive heart you will ever meet. Some people have hearts so sensitive they feel every little thing, and shyness is their defence mechanism. It might be that life was waiting for you to come along and boost her confidence. If you duck out now, you may have missed an opportunity to make the world a better place.