I would just impulsively suggest that we do something together. If she mentiones something that she likes doing I’d suggest that we do that together. If I am doing something and she seems interested in then I’d suggest that she joins me. I would even suggest that we do something and if a better idea comes to mind we’d do that… The less I think about it the better. Seriously just talk to her and be willing to say whatever and do whatever. You two may end up doing things that you wouldn’t think that you would enjoy and you end up enjoying it… Or neither of you enjoy what you’re doing so you can suggest that you leave and do something else. You can even ask ” hey would you like to do whatever sometime so I could get to know you ?”. Think about it… If I girl asked you out like that you would probably like it so why wouldn’t she.
If you make it out not to be a big deal she’ll feel more comfortable about going out with you. The moment you stop worrying about what you’re thinking and what she may be thinking you’ll start having a great time with girls.