Well, you both are sitting on your hands waiting for the other to make a move...but the problem is that neither of you is moving forward.
So, since you're the one who posted the question, I'm choosing YOU to be the initiator in communication (girls are generally better at conversation than boys anyway), ok?
You're going to have to bring up things for the two of you to talk/text about - First, how much do you know about him?
Stuff you can bring up as conversation - find out what some of his favorite things are (music, games, food, movies etc.).
Hopefully you two can manage at least of couple of convos that way...and maybe, after the two of you get the conversation flowing, he might ask you out.
But, remember, shy guys are very hesitant to talk (like pulling teeth) so you'll have to assume that responsibility if you want to have a relationship with this guy.