I generally live in fear of such moments. I’ve found that preparation keeps them from happening. Of course, every once in a while you can’t help but mess up. At those moments I look people in the eye and pretend (well not pretend) that I’m used to messing up and it’s no big deal (which, of course, it is).
The worst, though, was when I was a teen, and I never asked a girl for a date because I was so embarrassed that she would say no, and I would get a reputation as a loser. As it happens, that was probably the right move, since when I asked girls out later on, they almost universally said “no.” I learned how to not ask people out, while still asking.
Like my first girlfriend who I met on an outing club trip spelunking. She really couldn’t avoid talking to me when we were stuck together underground, waiting for the people ahead of us to ascend the chimney. Not a date, but just as good as one.