Whats the name of the issue here?
Bad inner game.
Sorry to say so, but If you have this problem, its becausue you are;
A Fucking WUSSY
You got mad at me for saying it? Good the first step to recover from your AFC status is to be angry and dissatisfied about it.
You wanted to talked to that girl on the plane?
I'll bet you did
But you werent able to do it...you wussed out. You were scared about something.
Yes: you were scared about
fucking up!!!
You were so fucking scared about saying something...and embarass yourself.
But all that is just on your head, hardwired into your mind. You can succeed!!!
Ten thousand years ago humans lived on 50 people communities. So, lets say half of them would be dudes. Of the remaining 25 girls lets say 10 would be taken, and 6 would be too old and 6 would be too young. Just 3 girls would be avaliable.
If you fail courting one...all of them will know about it...maybe even the whole village finds out about your failure, and you will become a loser, the village idiot, no girl wants you now.
So, your genes say that if you fail with one girl its a big deal. But in the 21st century, so if you fuck up with a girl...well it doesnt matters cause there are millions more to game!!!
The first step to get confidence around girls...is to improve your inner game. It is a long process, it requires lots of disipine, and commitment, int short: it isnt easy.
If you start improving your inner game, your life would improve, not only on the relationship-sexual area, but in many other aspects of yout life, like your career.
I recomend you to start reading... almost every PUA book talks about inner game.
Wish you luck...And may be the force with you

, really: you are going to learn to have "The Force" on your side...thats inner game about.