Most Helpful Girl
since the issue is about two people potentially dating, the matter should be between those two people only because it's really not anyone else's business. when i was single and looking for a relationship, I would ask the guy out when it's just me and him or I pull him aside to someplace mire private. If the guy were to ask me out, i would prefer if he didn't do it in public.
Another reason to ask in a more private setting is that maybe the girl doesn't want to date you or isn't interested and they would be more willing to let you down in private. When you ask a girl out public, sometimes the girl doesn't want to hurt your feelings front of others and may actually say yes and then ditch you later (i know ladies that do this).
Most Helpful Guy
You think to much about it. Make your mind blank and say to yourself: I CAN DO IT. Then just go for it!
Whats the worst that can happen? They laugh at you? You won't see them again anyway ;)
GL, stop being in your head all the time!