As you know, coremelt, less is more.
I think you can convey all of that with “can I fall in love with you?”
好きになっても良いですか?
I don’t know how old either of you are, but there’s a well-known Off Course song from 1980 called Yes/No, and the chorus goes:
君を抱いて良いの
好きになっても良いの?
kimi wo daite ii no (kim-ee oh die-tay ee no) May I take you in my arms?
suki ni nattemo ii no? (sue-key knee nah-tay ee no) Can I fall in love with you?
The song is all about the hesitancy a guy feels as he tries to figure out whether she feels the same way. He alternates between expressing his feelings, coming juuust this close to asking, then gets nervous, backs off, but then sees something that gives him hope, etc. They’ve known each other awhile, and he is freaking out just a bit at the thought of losing her if she doesn’t feel the same.
One thing. The ‘no’ at the end of the phrases makes this a question, but it’s pretty strong–it can come across as ‘well, is it okay or isn’t it?’ If you do use it, speak slowly, and don’t emphasize the ‘no.’ Then it’s kinda cute. Or you can make it a bit more polite with “suki ni natte mo ii desuka” or drop off the kimi (you) and just say “suki ni nattemo ii?”
NOTE: the first part of the chorus (kimi wo daite ii no) uses the verb ‘daku’ which means both ‘hold’ and ‘have sex with.’ Please, for the love of all that’s holy, wait until you get a yes to the ‘can I fall in love with you’ part before trotting this one out.
Here is a link to the lovely song (I’m an old sap). Please excuse the crappy sappy video.
As others have pointed out, you could just ask in English, but if you’ve been speaking exclusively English up til now, this’ll be kind of sweet–showing her you’ve gone to the trouble to figure out how to ask in her language. But speak slowly! If she expects everything that comes out of your mouth to be in English, it might take a couple repeats before she realizes what you’re saying.
Good luck! がんばってください!