Tl;Dr: Approached girl who later told me she just wanted to be friends. This has happened a lot recently (every time basically) before I can set up a date. If I can get over approaching I usually fall back on "hey I think you're cute can I have your number?", get the number and leave. This usually gets me numbers but nothing after! Please help!

I've been an on/off lurker for a while and posted what I thought was my first #close a while back but turns out it wasn't. Since I've approached a lot more girls but it always ends the same: with nothing! I'm starting to get discouraged so I was hoping you guys could give me some feedback on my most recent failure:

There's this girl I saw a few times on the subway to school but never really checked her out because she always had her face in a book and I didn't want to be obvious. Turns out she's gorgeous and so I see her walking to class at school as I'm walking out of the office. I quickly decide to approach and tap her on her shoulder and this is how our conversation went:

Me: hey, my name's redplayer

Her: my name is jess (actually it was a harder name)

Me: Jane?

Her: just call me J

Me: OK well J I think you're really cute and I wanted to know if I could grab your number

Her: uhm...sure

At this point I kind of forgot the conversation but I recall she was playing with her hair. I asked a bit about what she's taking but before long (less than 2minutes) we hit her class and I had to say goodbye.

Usually right after I get a number I'll text a short message with my name like "hey, its redplayer :)" or something. I usually get responses back quickly but I got nothing and assumed it was a fake number. Then this morning I saw her at the subway and said hi and she told me she thinks she gave me the wrong number and so she fixed it. I tried talking to her but she had a midterm to study for so nothing was said. Later in the day we had the following text convo:

fixed number around 8am

Me (10am): hey its redplayer, how did your midterm go?

Her(10am): it was good! also I just wanted to let you know I'm not looking for anything besides friends and I didn't want you getting the wrong idea haha

Me(11am): that's great! And we haven't even had a proper conversation yet and I'm already your friend?

Her(noon): yeah, I'm pretty bold like that

Me: (130pm) wow, I wish I was bold. Let's grab coffee Friday morning and maybe you can give me some pointers

Her(730pm): sorry I can't my Friday schedule is really weird! Sorry!

at this point I decided to be really blunt

Me(730): great! I hate coffee! :p

Me(seconds later): I'm going to think up something else we can do but if you're not interested in hanging out platonically, at first, then you can preemptively say no

Her: I like the long words! But sorry right now I just have a lot on my plate so I'm going to have to say not right now

this point I decided maybe I could salvage a friendship

Me: wow that's a pretty nice rejection

Me: I'm pretty friendly though so if you're free later on let me know and maybe we can do something.

Her: haha ok! :)

That's basically where I left it and so I'm wondering what tips you guys could give me. I know one of my weak points is the first contact. I never know what to say and its stuck in my head to get in, get the number, and leave. If I think about it at all I get AA and end up missing the opportunity. Also this is the 5th or 6th time its happened and I'm starting to get discouraged.

That main thing I'm hoping to get help with is:

-What to say to them initially

-What to do after

-How to set up the date

Also I know you guys aren't big on settling for friends but I'm in university and I think having girl friends can get you introduced to more girls so if there's a way to recover and be friends that you guys know that would be a great help as well, especially in this situation!