Hello there and :welcome: to the forums!
Your female is beautiful - what's her name?
Is she actually biting (painful) or just nibbling (not painful)? If it's just nibbling or it's a mix of both, she's probably trying to play with your hand. Sometimes they get carried away and bite (my budgie used to do that) but if you nudge your hand away when they do this and gently say "no", or put them back in their cage and leave the room when they bite, they will learn that biting sends you away and they shouldn't do it. It will take a bit of time to train her out of it but if you're gentle and consistent her behavior should change.
Also, you've come to a great source of budgie information and it's great to have you here! Be sure to read through the many budgie articles and "stickies" (threads "stuck" to the top of each subforum for easy reference) to ensure you're up to date on the best budgie practices. If you have any questions after reading through things, please be sure to ask as we'd be happy to help.
I hope to hear updates on how your little one is doing :sky blue:
Cheers :wave: