Need Help with Girl I Met at Her Work

Ok so I'm not really sure where I stand here..

I've been talking to this girl that works at the Paradise Bakery up by my school for a couple weeks now. She's been working there for a while, but just a few weeks ago I noticed she was being extra friendly and flirtatious. I wish I could have been a little more quit on my feet and just casually asked her out at the time but it was tough since I'm sort of a regular customer there. I started going in a little more frequently and we'd have good conversation..we found out we actually have a lot in common as far as school and hobbies go.

Anyway, I did finally ask for her number about 2 or 3 weeks later, only after she was telling me about these rock climbing classes she takes and told me I should come try it. So I met her for the climbing classes, all went good and she got me to sign up for them. (maybe I shouldn't have?) Then, after the class I invited her to this party my friend was having later that night. She seemed a little hesitant about going but said to text her. When I texted her she said she really wanted to go but that she had a lot of homework and that she had school early the next morning (which is both true - pre law student) I told her fine no problem blah blah....then no response. I was expecting a little more but whatever.

Later that week I texted her up to confirm on the class time she was going to. She said what day but wasn't sure on the time. She was really responsive this time (lots of smileys, etc) and told me she would be sure to hit me up and let me know. So that day rolls around, and I never hear from her! WTF?! So I said fark it and just went to a different time frame class. Should I have been more persistent and texted her to ask again??

So far I haven't really escalated at all (my biggest weakness), because I was always worried about that weird employee-customer line I had to cross. I don't think that I've done a good enough job at conveying my interest but I'm sure I haven't been shuffled into the friend zone yet.

So where am I supposed to go from here?? Should I go to her work? Should I text her this week and ask if she made it to the class? Is it too late to just text/call her and ask her out on a real date? I'm not too worried because I have other girls I can fall back on but this one is my BIG crush, so I'm trying to play it careful here. Somebody give me some guidance!

Invite her

As in on an actual date?? Or just casually invite her to go somewhere? I feel like I SHOULD invite her out casually but I am avoiding FZ at all costs this time around