I would first like to note that I am a freshman at a math and science university, and, as you might expect, a lot of the students there have little to no dating experience, my self included. The girl I am interested in is Korean, although she attended an all girls Catholic boarding school in the states. She comes off as extremely shy, and I suspect that she does not have a ton of dating experience either.
Anyway, about a month and a half ago, I somehow managed to start talking to her, and we studied in the library together. Afterwards, she gave me her number (although this is common practice in my school, so at the time I was not sure if it was a huge ioi). From that point on, whenever I would run into her, she would seem to go out of her way to say hi, but she seemed very nervous about doing it. At the time, I was just getting into the PUA community/dating scene, and I made the huge mistake of not trying to get closer to her, out of sheer nerves and anxiety. Throughout this time, I would occasionally message her on FB, but she was always slow to respond, and sometimes would not at all. However, she would also sometimes reply very eagerly and invitingly. This only added to my confusion. Looking back on this time period, I feel that she was expressing interest, and that I could have done something if I would have sucked it up and went for it; sadly, I was not mentally prepared to do this at the time.
Eventually, she started being pursued by a much more woman-savvy classmate of mine, and she seemed to be very interested. She also stopped greeting me when I ran into her; I was devastated. During this time, I avoided talking to her much because I did not want to lose the tiny amount of progress I had made.
Now, the classmate that was pursuing her has told me that he is no longer interested (which makes sense because he seems to be very high energy and outgoing, and she is quite quiet and shy), and that he is basically cutting off communication with her until she gets it. I'm sure she is going to be feeling disappointed, and I feel that I might have another chance to make something happen. However, I do NOT want to make the same mistakes again, and I am therefore asking for your wisdom. Do I:
1) Come on strong (seems risky because she is very shy and I could imagine her being scared off by this)
2) Take it slow (seems more sensible, but I'm not sure how to basically "restart" our interactions; in other words, I don't know how I can just start talking to her and slowly expressing interest without scaring her off or making her think I'm a creep)
I have become much more self-confident over the last 2 months or so, but I am hesitant to try a bunch of the mainstream techniques discussed on this forum because, as I said, she has limited dating background/is very shy, and I have no idea how she will react to such behavior.
Thank you for reading this (way too) long post, and I greatly appreciate any advice you may have for me.