Should I even bother asking her?

FlightAuror2
So, there's this girl in my Positive Psych. class that I really like, she's got a completely different perspective on most everything, she's Gorgeous, and very funny. I'm very timid, I've only ever asked one girl out to anything and that doesn't include the only girlfriend I've ever had lol

Anyway, one day I noticed her in the store on campus and walked up to her, started talking to her about the class, introduced myself before leaving and she did the same. Since then she's sat in front of me every class except for last week (I sit in the back on the penultimate row against the wall furthest from the door, she told the person who sat behind her in that last row that because she had her guitar with her, she didn't want to be in the way, so she chose to sit there, inadvertently being in HER way...)

But she always says hi or smiles and our eyes always seem to meet somehow either before or at the end of class, and I noticed in the last class that she'd looked further toward my direction than necessary at many times, and I just figure there's probably nothing here, and she's most likely totally out of my league, despite a few of my friends saying I could get anyone I wanted, I just don't believe that statement, seems too good to be true.

There's a guest speaker coming to campus and we've both got tickets and I'm thinking of asking her if she has anyone to go with, I just don't know if I should bother lol any advice? It would be very much appreciated!
Updates:
+1 y
I was hoping to see her in class today, she missed, which I was thinking would allow an even better opportunity - ask her if she'd like to copy my notes? There's a two hour window from class to the speech, which is Wednesday, maybe offer a coffee/tea too?
Should I even bother asking her?
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