It sounds to me as if you aren't respecting her personal space regarding your hands. You need to train her to accept hands and realize that they are not there to hurt her. More often than not, we force our desire to have physical contact on our parrots when in reality they would rather not be constricted by our hands - especially considering that they are prey animals.
I trained both my IRN and GCC to accept hand cuddles by gradually moving my hand closer and closer to them. Anytime they showed discomfort, I would stop moving my hand close and reward them for letting me get as close as I did. Eventually I was able to place my hand over their bodies, and extended the period of time that my hand stayed on their bodies. You have to realize that being touched by hands is not a natural thing for birds... their form of "cuddles" is standing side-by-side with another bird and being preened, not having that bird open their wings around them and constrict them with their wings.
Learn your bird's body language. Realize when she is uncomfortable. Birds only bite when they feel their feelings have not been taken into consideration and you aren't listening to them, that or when they are overly excited/aggressive.
Train your bird to realize that hands are safe and result in rewards (such as food).
And, considering the age of your conure, you may be encountering hormones. When birds undergo hormones, they often bite for no reason that us silly humans can comprehend
. So that's also something to consider.
