I fucked up but wondering if there's any shot

Cold approached a girl, explicitly said she was cute, she's from another country, got her info. We meet up for drinks and have quite a bit, we talk, we laugh, we enjoy. Everything is going great, she's opening up, I'm opening up, having a great time, we're sitting incredibly close together side by side, our hips and legs touching, some kino going on with my arm behind her on the loveseat and moving towards her waist, I'm touching her knee and leg every now and again. At one point, something spilled a little and I even basically groped her with a napkin down in her groin area and lingered down there (which she said was sweet that I did that for her). She's not only beautiful but I actually really like her, I'm totally interested in what she has to say, she's smart and artistic and genuine.

Suddenly she tells me she has something to say. I ask her what it is. She says she has a boyfriend back in her home country. I just say 'oh ok', and she says she was afraid I wouldn't like her anymore, and that a lot of people don't want to see her anymore because she has a bf. I just remain as composed as possible, ask her how long she's been with him. She says 3 years. Fuck. So I ask if she's going to get married, she says no way, she just likes that there's someone to love each other. I recall that I tell her that I really like her and that when I met her I said she was attractive.. she says something along the lines of how she really likes talking to me and she doesn't want to stop doing that, and I tell her that I like her too but also really like her even more than just being friends and that I don't meet many people I connect with like this (which is fairly true).. she says "well, then you'll have to convince me" - I remember that very distinctly.

[just as an aside - wtf, right? she totally should have said she had a bf to start with when I first met her]

Anyway, I flirt with her some more, give her a peck on the lips a bit just really spontaneously. She laughs, we're having a good time still, and her signals (however mixed) were still flirty and open so I took that as just go and see what happens.

Here's where it gets shitty. By this point, we've both had a lot to drink and we leave the bar and get in a cab. I can't remember the next part too well but the next thing I remember after some time, apparently, is that we're both in the cab and she's now angry at me about something. She starts getting antagonistic, saying she doesn't know me out loud (like pretending we had literally never met at all), and I just ask her what's wrong and why she's saying that since we obviously just spent time together having fun and getting to know each other. I go in with her to her hotel and as we sit on her bed, she says she's sorry and I say the same. We sleep in the bed together, no sex. I'm kind of cuddling/spooning her (her head on my arm). Next morning, we wake up and I feign a sort of headache (I had a slight one but not as big as I let on) because I felt awkward about the whole thing, not knowing what to say, not remembering exactly how it went down, and especially that I somehow made her upset. I stay awhile and she seems totally open and ok by this point. I rest a bit due to my headache and we make a kind of smalltalk, definitely not as rich as we talked last night but that's mostly because I have this headache and just kind of trying to sleep it off.

I stay a while, she goes out of the room to shower and she comes back (fully dressed). As I leave, some more smalltalk and then she offers up the suggestion to let her know to go see a movie we both talked about seeing together last night. I say yes, of course and I'll let her know.

I did that about 4 days later to give it some time, she never replied.

Now here's a couple things I'm aware of: I don't have major moral quandaries about the bf part. I know for a lot of people this is way more investment than necessary due to either the bf or the awkward scenario that occurred and it's simply not worth it or that I simply blew it. But is there any chance, however small, that I can recoup any loss here or make up for it somehow? I mean, at this point I figure I have nothing left to lose so why not just go all out? This mentality is much less risky now than it was before, though I'll have to keep it in check the next time.

I had thought there were a few ways to do this: Write her an apology, just a pure apology, not asking for anything at all, not even to see her again. Just an apology and so it has purity and can be taken at face value, and see if she replies. Or still write her an apology but also mention how I would love to see her again since I felt we did have a connection, that I remember her saying how much she liked talking to me and that I feel the same way, and that I still very much would like to show her around town. Or totally ignore what happened (like I/we did the morning after) and ask her again to the movie but for a planned later date. When I originally asked, it was for the same day and it could have been too short notice (though if it was, she would have asked to reschedule herself if she really wanted to go, and she also doesn't know anyone here or have major plans so it's not like she's busy so...)

The only thing I can attribute the awkward scenario to was that I probably insisted that I go back to her hotel with her and just don't remember saying it until it was already said. And I can attribute this behavior to a past experience just a few months ago where I basically met a foreign girl completely randomly in a train station from a cold approach and F-closed her the same night in her hotel. So maybe I was insisting on this subconsciously due to this prior experience, which fucked it all up. And to some extent I can attribute the general behavior (during and post-taxicab) on both our parts to being drunk, right? I doubt I would have upset her or she would have reacted that way if we hadn't been drinking so much, perhaps. But in any case, I don't think I have sole ownership of fucking up here. She really should have told me she had a bf to start with. One reason she didn't may be because she wanted to make friends here since she doesn't know anyone but that's still no excuse because she's bound to say it at some point anyway, which would cause a barrier regardless and makes it worse if it's said later (like now), and she knows my intention is obvious since I already told her I'm attracted to her to start with so withholding that info isn't fair.

Look, I'm not in love with her. I know this. I know I'm going to get responses that say I'm obsessing on her. Ok, I get it. Either way, I realize you can call this oneitis or whatever you want but I'm wondering what I could do now that there's seemingly nothing left to lose. And I do have abundance so it's not about that (meeting a girl tonight, one this weekend, a few I'm in contact with, and others yet to call). Though out of the girls I've met these past several months, she's actually someone who is just my type and has a lot of the qualities, both inside and out, that I really like.

tl;dr - not sure how to tl;dr this but girl and I hit it off, suddenly says she has bf, gives me mixed signals, I somehow make her upset, how do I recoup?