blushing can be endearing, however if it's too easy to do you might need to get out more. Blushing once in a great while is fine, but if this a regular thing that is an issue, Women love confidence and if it is too easy for you to get flustered that's no good.

Use that to your advantage; "just blushing because you're cute" or something to that effect. Sometimes you can use awkwardness as a strength

Tell him he's very observant and then ask if you should ask him for the girls number or her.

Well OP, some people would find that really cute. Maybe she did too :) it's a clear sign you're bashful around her, meaning you like her, most would assume. Just play it cool, you'll be fine

My question is if you asked her out, wouldn't you naturally end up talking later? Isn't that what happens on dates?

I hate it when people do that... I mean I know I'm blushing why do you have to point it out?