If you personally cannot screw up the courage to go up to a girl and ask, to her face, to look in her eyes, and ask if she wants to go get a Coke with you; go to the movies with you, then how are you going to handle the actual dating when you have to talk to her face to face? Bury your face in your phone and text her while she is sitting next to you? The worse thing that would happen is she would say No.
Be quietly confident. Lift your head up, smile and while you are looking at her like she is the most beautiful girl in the world and simply ask if she would like to go get some ice cream (or whatever).
Each time you do this, you will gain confidence. You will not gain anything by passing her a note begging her for a date.