First, that "date" line is most likely too foward and direct for any girl you first meet. The thing about Japanese girls is (most) like to play the slow game. It'll take about 2 weeks before you are really where you want to be if you work at it and can hang out a lot.
Heres my plan. First, get an idea of something to do. I don't usually say "lets hang out" unless im too busy to hang out with a girl in the near future. Otherwise think of something FUN you can go do together. Play up the gaijin angle, they are diggin it anyway.
Do whatever it is you think is fun. Hell, some girls even just want to drink, and you can have a relationship with them based purely on drinking together (and what comes next).
お名前聞いてない - I haven't heard your name...
ケイタイ持ってる?- Do you have a cell phone?
Get that cell phone number and set up something fun and the rest is gravy.
Edit: I I forgot the iceing. If you can't think of anything fun to do just say, "Maybe you could teach me Japanese and we could study together" or something along those lines. They know Japanese, you are learning Japanese, that's an instant connection and way to get inside their social bubble (that at the moment has you as a stranger, not a friend/study friend). After that it's up to you where you want to take it. Get a bunch of different girls to hang out and study with, then pick the one you like the best and turn on that western charm and *BAM* you got a girlfriend.