Possible Rat Territorial/Anger Issues?

Question
Hello!

Just over a week ago I got 2 pet rats from an owner who had to rid of them, and through them I also found out they were pet store rats, they are both female and approximately a year old and are both sisters.
One of them i get along quite well with, although she dislikes being handled she loves to sit on my shoulder and play, I've bonded with her really well and she loves me.

But her sister is different, I've done everything I have done with her sister and I have not done anything to upset her, I've been really gentle with her. But every time I put my hand (even just near the door) in or very near the cage she'll come up and bite me. It's bitten through my nails several times and drawn blood all over my hands.
I just can't connect with her. I won't pick her up against her will at least until she gets more comfortable with me, for her sake. I can't find any real information on how to train her other than while she's eating treats pet her then.

I would love to keep her, but if I see no improvement in a significant amount of time then I'm going to have to find an alternative (of course I would try to find the best)

The rats themselves don fight between themselves and are very loving towards eachother.

Do you have any information on how I could perhaps train her not to bite and let her be as comfortable with me as her sister? And I'm also looking into possible adding another ratlet to the mix if things get better.

Thank you!

Answer
I would almost bet that these rats were mistreated or neglected in some way, perhaps the quiet girl more than the assertive one.   This happens so often and is very sad.  The shy girl bites out of fear, not because she dislikes you.  

I am so happy to hear that you are willing to work with her.  I know if countless rescue rats that started out as aggressive or biters who, with time and patience by their new owners, overcame that and became wonderful pets.  Of course there is no guarantee but worth your efforts.  I hope you will not consider giving her away should she continue to fear you because these two girls sound very bonded and how sad for the friendly girl to lose her lifelong companion.

I have a wonderful website on trust training.  The best I've ever run across.  
http://www.joinrats.com

Getting a third rat is actually a very good idea, regardless of whether your fearful girl overcomes her fear or not.  I always keep three or more rats at once in the sad case that if up you lose one suddenly, the other is not left alone and depressed.  As well adding a third may actually help the your quiet girl in overcoming her fear and trusting you more.  Rats are social creatures and the more there are, the happier they all are together.

Please again keep in mind that trust training will take a lot of time and effort and continuous patience, and it sounds like you are willing to give that.