Dude,

you were too careful! Girls like when a man is confident and makes a bold step. Starting a facebook convo is not the boldest step you can make. Next time you see a girl you like, why don't you just go up to her and say: "Hi, I've noticed you standing here and had to say hi. What's your name?" If you are completely confident while doing that the response will be amazing. In fact, you don't even have to say all this stuff. A smile, eye contact and a confident "Hi" can be enough.
The guy on whose lap she was sitting probably DID make this bold step and this is why she was sitting on HIS lap

Of course the confidence thing is for some of us easier said than done. But this is the work you should do on yourself and it's a journey. But starting a chat in FB won't bring you closed to your goal.

Hope this helps.
Ivan.

why not ask for her phone number on facebook and call her and ask her out for a drink?

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Life is for living, so I ain't giving up!

So, I wrote her yesterday and asked her for opinion about something and she said: I was just about to go off... Some other time

So I decided I'll just let it be. There are so many other beautiful women that she just isn't worth it. She's got him now, so I'll just wait, cause as much as I know that guy, there's gonna be no serious realtionship. And afterwards, I could try again, a new start, with more experience. I'm sure it would be possible to get her instantly, but not with my experience I guess. That guy is just too alpha.

It's not a problem that I wouldn't be confident enough. I don't really have problem with women, I've been with women. It's just about some certain women and women which I don't know. I will defenitly not approach the same way again, on her or on any other woman. Thanks to you, guys.

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Stay cool.