Online? Nope! (Although this is how my relationship initially started - but that's different!)
Since you know her, you're going to be scared. It's so very understandable. And you do need to just suck it up and ask
Because if you don't, and soon, you'll think this to death and overanalyze it and make it into this big huge thing. So do it soon! And not online
Next time you see her, just ask! Don't think about it, just do. The sooner you ask, the sooner it's done. And you won't have to worry about it anymore