So I know this girl. We were in a math competition together in the same team (got third place too) and I found out I might kinda like her.

So this morning, I went to see her in her class before lessons begun in the school and starting social proofing everyone there (it was a small class of 11 people) and moved on to her,... and in the middle of our interaction, I went :

PUA : So, when are you gonna invite me over to your place?
HB : (gives a surprised startled look) Why would I invite you over to my place??
PUA : OMG you forgot?
HB : forgot what?
PUA : Our 'Titanic' movie date? (The day of the math competition, we were hanging around and talked bout good movies. She mentioned Titanic, I mentioned I've never watched it and she goes "No way! How cna you not have watched titanic??". So I go "are you saying we should definitely watch titanic together sometime?" and she says "yea!!"
HB : Owh yea!!
PUA: So,.. when's that gonna happen? (with a sly smile)
HB : I have your number right so,...
PUA: (cut her off) Tell you what, you gotta give me your number else you'll forget bout our date
HB : Okay,..

She then goes into her bag to look for paper but in the end decided to srcibble her number on my palm. (+1 for me )

So I n-closed and left her class. At the end of school, I bump into her and I'm like "and don't forget,.. call me!" I was actually kinda worried bout this move, at that time, I forgot asking the HB to call was risky cause she might not call.

But this afternoon, she called and we chatted a bit. And thats when she said

HB :Are you gonna come by my class again tomorrow morning?
PUA: Well since you enjoy my company so much I will
HB : Don't,..
Pua: (kinda taken back) okay,...
She then mentions something bout her friends saying we're flirting (clear sign of ASD)
PUA : okay fine, I get it
HB : are you serious about the titanic date?
PUA : are you?
HB : I dunno,.. well if your serious about it
PUA : Well I guess I am

And little bit more fluff talk and we say goodbye....

Now,.. this isn't our first interaction. She has given me quite a few handfuls of IOIs but today just kinda took me back a little. I'm pretty sure I was gaming the whole class and not her alone. And we were flirting! I know she knows that, she's a really intelligent HB so why does she wanna stop? Is it just cause she wants to flirt in isolation without all her friends and classmates??

I'm kinda dunno what to do right now. Should I still go visit her class in the morning? Or should I just back off showing non-neediness.

Dude, you embarrassed her in front of her class. I'm surprised the girl is still interested. That's a big point for you!
In my opinion, you shouldn't back off. Just don't be "public" about your interactions with her.
Anyway, so what happened? It's been almost two weeks now.