Gabriel- I am going to agree with la_esperanza on the dinner. But you will probably get told "no" a time or 2.
I went through this with H. I had asked him out a few times and was turned down. Finally I got tired of being turned down so I stopped asking.
Well, low and behold, I decided to do something one night and he had commented about NOT being invited and I simply said "I got tired of being shot down so I said the hell with it."
He ended up asking ME to do something. But one thing is for certain........it can't hurt to ask. If she turns you down simply smile and maybe say something like "ok...maybe some other time."
Things do take time and you won't know what you will get until you try