You have been watching too many Bollywood movies. People don't ask each other out. If they are interested in someone they tell their parents, who send the other person's parents a rishta, and things go from there.
lol that made me laugh.
but seriously if your invited its usually a good idea to go. That way if you didnt enjoy it you can not go next time, at least you know.
Asking to meet up with someone cane be tricky as you say without looking desperate. Maybe you can find out where they hang out and "accidently" be there, then just go over to them and say hi, etc.