haha, I personally think this is a cute thread ;D
well it's like seeing my boyfriend and I when we first started to hang out together :P (btw I'm a japanese girl and my bf is a swede - extremely shy one, too ^^)
so I don't think you should be too bothered what to talk about with her and hey, since she's new to sweden and your town, you could just show her around and have fika?
that way you can hang around with her and no need to "ask her out" which would take a whole lot of guts? :P I'd think it'll be a good excuse. or ask her if she wants to exchange languages with you? you could teach swedish to her, and her, japanese to you :3 benefits for both two, right? (and of course especially for you!)
I just think you shouldn't be too worried or frustrated on these kind of matters - just take it easy and let things happen!
that's what I did with my bf and now we're together, soon 1 year anniversary xD
anyways, I hope you'll get more chances to meet her and talk to her! lycka till ;>