I went to a date with my classmate who just ended very serious long-term relationship. We kissed that night, she told me to call her and I did.
After I kissed her on that second date she asked me what my idea of this relationship is. I said that I wasn't really thinking about it and just wanted to let things develop naturally (my first mistake - I already knew why she's asking). She explained to me that she's not looking for nothing more then FWB and that she is already in the same situation with at least 2 guys (both of them live in different country though).
I was such a retard that day that I went on and on talking about stupid stuff and eventually thought that it wouldn't be such a bad idea to tell her about this other girl I'm in "relationship" with. I'm writing "relationship" because we don't have much time to see each other right now and there wasn't much intimacy between us since it started. It will take a very long time to progress but it's worth it (20y/o, beautiful, virgin, the best personality ever).
Well anyway... that whole evening was pretty horrible, we were just exchanging our opinions about relationships and some pseudointelectual nonsense (she's like that).

When saying goodbye I told her that I would like to see her on Friday and hinted sex. She laughed and said that I should keep this stuff for the other girl but that she can always find an hour-two-or three to meet me (her words).

Later I apologized on FB for sounding so stupid, she laugh it off in a friendly way and we haven't spoken since.

Is there any way to rescue this shipwreck?
There is a time limit because she may leave in a month or two and if that happens I would see her only 1-2 a year. Not really worth maintaining imo. Although she is a great person I would like to keep in touch with her.

So she said she's in the "same situation" with two other guys. I presume they're FWBs as well? If so, then you should look at it as a shit test. You could have shrugged your shoulders and given the impression that not a single fuck was given that day. Or you could have also told her how you're seeing another girl as well. Both are adequate, so you didn't mess up there.

Where you messed up though is apologizing. Why? And for what? Don't feel bad and don't give a fuck for whatever it is you said. You were just being yourself and honest, and for that there is no shame and nothing to feel bad about. Anyway, she said she could manage to find an hour or two or three to give you... So I don't think she's entirely avoiding you.

It was more the way I told her about the other girl. I've made a HUGE deal about it.. imagine Clint Eastwood looking deep into your soul and saying "I have something to tell you...". She even said that it seemed like I had something very serious to tell her when I said that.

I was set on banging her this Friday. I might still be able to convince her to come to my apartment, have a dinner and watch a movie or something but then what? Should I just focus on "buddy" in the word "fuckbuddy"? Have a good time, keep it light and don't go any further then first base if that?

My internal compass tends to always lean on the "nice guy" side. That's why I would not suggest FWB to her myself even though it would be perfect.

Well okay, you were serious about it. And what of it? Did you have to deliver "bad" news in a softer tone as if you were telling a cancer patient that he's terminally ill? You made no mistake, therefore you should have no shame.

Just go back to the frame you had when you first attracted her, and when things were going well. Essentially, pretend you never told her about the other girl. That's your game plan. And never suggest FWB with a girl. Let it occur naturally.

But here's a more important question: if you want her as just a FWB, then why do you appear panic-stricken by the thought of losing her? What if you were losing the other girl... Would you be more panicked? If you had to choose one of the two, which would it be? Some important questions to think about.