Well, I got this one parakeet about three years ago, but it never learned to trust me and bites me a lot when I try to pet her.
I don't know why she is exactly like this, I got her when she was around two years old and all I know is that she was in a cage with about twenty other parakeets and never was hand-introduced at the store I got her.
I also just got a new parakeet for her company, he is still under four months (purple ces) and he's a bit shy, he just sits on the perch and does nothing really. I want him to know me, and I tried to hold him earlier but he bit my fingers.
Any advice?

If you're trying to "hold" a parakeet that isn't finger trained yet, it means you didn't read my website

Here are the pages on how to hand train your parakeet -

http://www.lisashea.com/petinfo/articles/bird_hand.html

go step by step SLOWLY through this and follow the suggestions, and read the other pages on the site too. That's how to tame your keets

Parakeets aren't "petted" like cats btw If anything, they are gently scratched under their chins and on their heads, but that only comes after they are fully trained.

Yah my pebbles dosen't like being "petted" as you said.