TheseDays has made a good point

If she was only nibbling you, and you felt her beak but no pinching "bite" sensation, she most likely either was trying to see if your fingers had any food on them, too, or if she was gentle, she was trying to preen your fingers.

However, if she was really biting you and it hurt, it could have been any number of things.
Were your hands in her cage? Many budgies don't like you to "invade" their space after they've fully and completely settled in and made it their home.

This could also come about because she is reaching puberty, which all budgies go through starting at 6-12 months of age, at which point her hormones will be higher than usual, causing moodiness, withdrawn behaviour, and slight aggression, especially territorially. If this is the case (which I think it is, as she is around 9 months old by now) then the best thing to do is to carefully watch her body language to know when she is okay with you putting your hand by her and when she isn't. Also, give her her "space", and don't put your hands in the cage too often. You can still interact with her, but during her moody period stick to talking to her and sitting close to her.

Generally in a few months everything is back to normal and she won't bite as much

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