The cage is definitely a nest at times. Being so new to you, it may take a while to get used to you. You can try adding a perch to the outside of the cage, and attempt a step up from there if she's familiar with it. If not, it will take a hands off, treat approach to make a connection with her. If she's biting she definitely doesn't want the interaction. It needs to be her choice to interact with your hands. Maybe look through the training section for more ideas.