Get her number and ask her what she thinks about going out this weekend. Don't say "hang out" say "go out". She will prob say "yes" considering you are right there lol but follow up with a call the next day. Ask her on Mon in person she can think about it. Then ask her wed. If she is still interested. Personally the longer time I have to prepare the better. I don't think monday is too eager at all. I think it shows respect. I would give the guy a two thumbs up. I hate last min. Guys. I don't do that.
I think you should give her a few days to figure out what she is going to wear, especially if she is pretty busy. It also helps build up some expectation. :) I think you're more likely to get a 'yes' if she has time to prepare properly too, since I would probably be caught off guard if I was asked to go out the same day you did the asking. It does come off as last minute, like you just sort of decided to do it on the spur of the moment. Making plans super far ahead would come off as a little odd to me if it was just a standard dinner out, but it would make sense if you were asking her to a concert or something that requires tickets or reservations. You can ask for her number first if you want, but a face-to-face is always more personal. If you are really nervous, go for the phone call though. Friday is probably the best day since she is less likely to have something huge going on the next day and you can stay out later if you two want (if she doesn't have something Saturday).
Wednesday is the best. It doesn't appear desperate and lets her know that you would like to make with her ahead of your friends, and shows that you are courteous enough to ask ahead so she can plan. It is not so far ahead to look anxious but, allows you to ask before any other guys do.