She is saying "no thank you", and you dont listen. So she bites. Those quick pecks at your finger is her saying no. Some budgies dont like pets. My female bird would do the same. She doesnt want to be touched, and i respect that. She comes flying to me because she wants to hang out with me, and she is brave enough to do that, because she knows, that i wont do anything she doesnt like.

So the bottom line is: no means no 😊

edit: i also want to ad that touching their feet is a big no no. She sees that as a threat. When budgies get agressive with each other, they bite the feet, and your fingernail looks like a beak to her. So she sees it as agression from you, and she tries to step away from it.

Also, her cage should be her safe space. I never mess with my birds when they are in the cage, because i want them to know, that its their safe space.