So you want to be this girl's friend but find her annoying? ???
If you really want to be her friend, then just talk to her, ask her how she's doing and whatever. Ignoring someone is usually something you choose to do, consciously or not. If you find her that annoying, a friendship with her probably wouldn't work out in the first place... Friends are not forcibly made. Some people just "click." Make up your mind about what you want and just stick with it. You shouldn't feel guilty about a decision if you think it's for the best.