I agree though, bank teller is HARD, can’t go sliding notes as they’ll think it’s a robbery note.\
OP, you reminded me that I did this once about two decades ago. There was a bank teller I saw on the regular (at the bank I mean) and got into light flirtatious banter with her. This was back when we actually deposited checks with deposit slips, which I did each week for the company I worked for. So one day I went in and wrote on the deposit slip asking if she'd like to get a drink some time. (There was no deposit, ha.) She smiled and wrote on it, then stamped it for effect and slid it back to me. "I'd love to but I have a boyfriend." Probably a smiley face or something too. Well I tried, but at least I could tell I'd made her day. This was all back when I was first getting my cojones back and learned game, reading articles on the old Sosuave and such. That polite rejection felt as sweet as a lot of victories for me and I still enjoy the memory as much as a lot of conquests. Unfortunately our office moved a few weeks later and I stopped going to that branch.
But enough of me, as for your experience, way to go and I think she was cool to follow up and apologize. She was obviously invested/curious enough to look you up and write you, that's a good thing. It's possible she didn't want to get in trouble at work but maybe she will find a way to seek you out on the sly. (Haven't yet read past page 1 of the thread.)
FYI, I'm not suggesting you wait around hoping or try again. You took your shot. I'm seeing some bad-frame advice from guys who are preoccupied with how many times she gets asked out, how many options she has online, etc. Who GAF.
Two concepts to keep in mind:
ALWAYS ASSUME ATTRACTION. Speaks for itself.
REJECTION ISN'T REAL. Guys thinking of all the reasons behind the reasons they get rejected are wasting their time. Most of this is nonsense and mental masturbation. Guys
judging her for rejection are really showing the holes in their game.
She brought a little positivity into your story, and you rewarded her by inviting her to bring some more. She declined for her own reasons which is her right. Your story goes on. I do recommend you follow
@Atom Smasher 's advice in tweaking your frame a bit. As I read on another site, the mindset should shift from "Please" to "Thank you."