Hi TweetieBird and
to the forums!
I agree with the great advice offered above. FaeryBee is correct, she is biting because you are invading her personal space without her leave or consent. By forcing her to interact with you in her cage when she doesn't want to, she will be more and more aggressive towards you as she learns that you don't have regard for her personal feelings.
You can stop the biting by not putting your hand in her cage when she doesn't want you to. You can tell she doesn't want you to when she makes angry noises and lunges before biting. Allowing her to leave her cage when she feels comfortable is the best way to ensure she is at ease. Putting perches on the outside of the cage like a "front patio" and putting a playground outside of the cage are both great ways to inspire her to leave the cage without you invading her territory.
Also, both genders display this sort of behaviour when they feel threatened and their space is being encroached upon, not just females.
Be sure to read through the links provided above as they will be of great help in ensuring you're up to date on the very best of budgie care practices.
What's your girl's name? We'd love to meet her when you get a chance
If you have any questions after reading through everything, feel free to ask as we'd love to help!
Hope to see you around, and good luck!