When to ask for a girl's number?

No, a guy does not come off as "desperate" by saying that. Saying that makes girls think. And that's a good thing.

Here's your problem, when you ask for it you say you don't do it confidently women see this and they think oh well this guys not a confident guy and if you hesitate they will hesitate to give you the number. It's so easy man all you have to do is walk up to her talk for a few mins, ask her if she's single, not do you have a bf, just say so are you single, if they say no I have a boyfriend then forget it but don't just run off, stay there and talk to her for a few more mins say it was nice meeting you but I have to go my friends are waiting.

Sometimes they will ask do you want my number. If that happens say sure and get the number but unless she's willing to cheat then I wouldn't call her unless of course you want a friend out of it.

Now if she says no I'm single then say let me get your number, once she gives it to you put it in your phone and call it to make sure its a real number. If you stay there and try and chit chat with her your going to get the awkward silence, so say well hey my friends are waiting but I want to take you to dinner next weekend and I will call you later this week to set up a time. In my experience I flirt with them first before getting the number and then they usually say do you want my number.