the picutres of Tweetie are fuzzy but she looks like a girl to me.
Also - the type of biting you are describing is clearly not the biting out of fearfulness since she is willing to sit on your hand. In fact, biting you while sitting on your hand is sort of a good sign because she is comfortable with you and not trying to get you away. She could be biting for several reasons. As coco's mama said, females are biters in general - so I would make sure you have plenty of toys that are chew-friendly in the cage. anything to shred like paper towels, or raffia, and of course a cuttle bone or mineral block.
When she bites you, she may simply be excited, playing, showing dominance, or just exhibiting her female biting "need".
You basically have to discourage the behavior without scaring her too much. The "wobble" technique is easy and used alot - where as soon as she bites, you wobble your hand so that it unsteadies her. You can say "No biting" when you do it - and i bet she will catch on quickly. They don't like that unsteady earth-is-moving sensation. I would try that - there are other techniques - but I think this one is very effective - let me know how it goes.