I agree with the guys who say to NEXT her. And this is coming from a guy who has made posts in the past about not NEXTing all the time!
What stood out for me is when someone mentioned she didn't even introduce you to her friends. My girlfriend, although we've been together only a relativley short time, has been trying to set up meets with me and her friends to introduce me to them and I have already met her best friend. I didn't think much of it as far as being an indicator of interest until this post, but none the less it looks like its missing from your brief fling with this girl.
The second thing is you have not mentioned weather or not you had sex with this girl or what physical moves in general were used. If you guys had a few nice "dates" that ended with you getting a kiss on the cheek - if even that - it probably means she didn't like you that much and had little to no sexual interest in you.
That is a key piece of info. If she was all over you and you did have sex or close to it, that's different. She may have had some reasons to leave you behind but maybe things can work out - even then its iffy but at least there might be a chance. Otherwise, forget about it. If not much physical action happened, you're not going to get anywhere with her again.
Finally, the FALLACY you are committing is the whole "I don't care that much, I just want to see how it goes with her again as an experiment". You are lying to yourself and to us, because you are OBVIOUSLY very attracted to this girl and you like her a lot. You aren't doing it to experiement for sh1ts and giggles, you are doing it because you are hoping it goes somewhere (you are outcome dependent).
So be honest with yourself, if you like this girl, go for it because you like her and want to be with her -- though we all strongly advise you against it because we've all seen this scenario play out a million times, none of which resulted in the outcome you would like. But go ahead, do it and find out for yourself, just know what you're in for.
If you are TRULEY wanting to just experiment, don't bother, again we have seen this play out enough times in the real world that we don't need a test subject to prove what we already know. Don't waste your time on it and get some action from girls who like you in the mean time. Then once you succeed at that you will have a much better story to talk about and discuss with us on the forums than your experiment with some chick who dumped you and got a bf.