I can see why this is frustrating for you, but your post made me feel very sorry for this woman.
Hmm. It sounds as though she has social boundry issues. But from what you have written in your post you seem to be overreacting to this ("physically can't look at her").
You have initiated friendship with this woman, and by the sounds of it she needs friends, and now you want to dump her with no explanation, and are getting annoyed that she is hanging around intruding on your much better friends and fun busy life. You say you don't want her to make you out as "a class A bitch", but to be frank, you do seem to be being bitchy about her.
Take a step back from the situation. Take a deep breath. If you have a busy life and lots of friends, I am sure you can find it within yourself to let this (lonely? Misguided?) woman know how much of yourself you are prepared to give her, in a sensitive, kind way.
Be firm and friendly and broken record about it.
"Yes, I am going to the school but don;t wait for me because I prefer to stick to my own schedule"
"Thanks for your text, no I can't do X this afternoon sorry" (no excuses)
As for the standing too close, "don't get too close, I don't want you to get my cold" should do, repeated a few times.
And if you are standing talking to your friends and she is standing nearby, the polite thing to do is to introduce her, not roll your eyes and ignore her.
Be a grown up.