New pig likes to bite?

[Lachesism]

I just got a new guinea pig about three days ago. She's not quite used to me yet but she sometimes lets me pet her and will eat from my hand.
She used to hide when I approached the cage but now she's less afraid. I was excited to think I'm making progress with her but suddenly she starts coming up to the cage opening and biting the bars and putting her paws on them until I come up. When I do approach, she acts like she wants to sniff my hand, and when I open the cage and let her, she bites. Not hard at all, just a little nip but I'm not doing anything like trying to pet her or holding food so I don't understand why she's doing this. She's done it several times, where she bites the cage until i come over and open it, seems like she wants to sniff me, and then nips me. At one point I let it happen for a moment, thinking she might just be trying to figure out what my hand was, but she kept nipping, and even got a little harder.
Why is she doing this and how would I go about stopping it without punishing her (I want her to trust me)

 

[Seven7]

Welcome.
She is a baby and might be teething. I would try herbs or veggies and train her to be polite using food.

I always hand feed herbs to my piggies and have never got bitten. I pet Finn daily, play with him, hold my hand in front of him, and never not bitten. Both Finn and Lara will give a little kiss when I put my hand in front them. I would definitely hand feed the baby and train her to be polite.

 

[HeatherRose]

I have one piggy that is super sweet and laid back but if you put your finger in front of her mouth she will keep biting it until you move it. Does she bite you when you are holding her or bite other than your fingers? I think mine just gets annoyed that it is not food and keeps biting until I take my hand out of her face! She is my calmest piggy and my 5 year olds favorite. She is so gentle other than that. My other piggies will nibble a little then start licking fingers.