OP how old are you? It's honestly really immature to be this caught up on some random girl you don't even know, and coming up with little "plans" on how to talk to her. I think you need to get more women in your life because this isn't healthy. If nothing ever comes of this, which is honestly a 99% chance (5 guys approach her a day dude and how many of them succeeded?), then you'll have wasted a serious amount of time and energy fixated on this all for nothing.

Download Tinder and hit some bars with your friends or something.