How do I ask a girl out in my cl?

I have this girl in my cl that I have been curious about. I thinks she's interested in a way because she laughs at my jokes, sits next to me, and makes little remarks toward me. She plays games on her phone all the games, and after cl she makes eye contact with me when we're walking out but I am too chicken because I don't know what to say or where to begin. I thinks she's interested, and hope she is. I don't want to ask her out during the cl time because it's cl time, and I don't want to p her notes because that's kind of childish isn't it? If I were to tell her straight up how I feel I would say this: "hey do you have five minutes to talk after class? My names xxxxxx, what do you think of the class? I always see you playin games on your phone haha, can I give you my number, i want to hang out sometime" I think this girl is exquisitely beautiful and looks unique for some reason. Do I tell her that? How the heck do I ask a college girl out in my class that I barely talk to? Ladies help me out!