The first thing to ask is -- does she break the skin when she bites? In my observation, cats bite for three reasons -- because they want to damage an enemy (or kill something), becuase they are suddenly frightened by something while you are holding them and your hand is restraining them (but in this case, they usually use their claws to launch themselves away from you, and they can really hurt you quite unintentionally), and because they love you and don't want you to stop whatever it is you are doing (stroking, cuddling, talking).
Assuming that your cat does not hate you, then assume the other -- love bites, either playful or during mating, are common behavior between cats, and when you share your life with a cat, you become a kind of large pseudo-cat to them. Most of my 16 have learned not to bite or to just put their teeth on some part of me mostly hands, fingers, forearms) without any pressure.
However, I have learned the following technique the hard way:
When a cat bites, I become absolutely immoble. I do not pull away or upset the cat with an angery voice or firm commands. I leave my hand (arm, finger) where it is, reach with my other hand and stroke the cat gently near the base of the neck, all the time talking softly (Now, you don't want to bite mommy's hand, do you? There, I know you love me. I love you, But mommy's skin is much thinner than yours...etc., etc. -- or you could try to recite the Getty'sburg address in dulcet tones) until the cat eases up. Then I very gently stroke the cat around the cheeks and lips and under the chin and then withdraw my hand from its mouth. I have the free hand there so I can add a little gentle prying power to my move, but it is rarely needed. The cat's motive is, first to indicate how much you are loved and accepted as another cat-type, and to keep you from moving away. They will also wrap their claws around your hand, or even catch the top layers of your skin, in order to hold you in place. If you pull away, they will dig in with teeth or claws or both, and you will be hurt.
I never raise my voice unless I deliberately want to startle a cat, because they take loud noises, commands and yelling, screaming, temper or sudden movements very badly, often becoming so frightened that they do serious damage. I never hold a cat tightly (unless I have to administer some kind of medicine, and then I use a towel around them to avoid getting hurt). I always give them the freedom to jump off my lap or disengage from me when playing. Even the tamest cats can sometimes get hysterically fight-and-flight on you if they feel trapped. Remember that a cat is not really a domesticated animal in most cases. That is what we love about them, isn't it? They are basically wild animals that have chosen to be companionable and we always have to remember to respect their right to stay or move on.
Try the soft approach. The fact that the cat changes its behavior to licking is a clear sign that it is trying another way to express its love -- that of grooming the object of their affection.