This is called resource guarding (you are the resource). It is very common and normal dog behavior, but you do absolutely need to deal with it. Fortunately, resource guarding isn't that hard to handle. Karen Pryor has a great book on called Mine! Here is a good article on it as well. In your case, you will need a friend to help you train this, because your dog isn't guarding from you, she's guarding you. Otherwise, the principle is the same.