Two introverts dating
So show him that you want something more - ask repeatedly.In general, you will need to carry the relationship up until the point that it is "official." When it has been established (or is otherwise clear) that the two of you are together, then you should start reducing your initiative and letting him take the reins.In other words, ask yourself "Am I attracted in spite of or because of his shyness? A very close friend of mine is extremely shy, and I know plenty of other guys that are shy. Shy guys, almost by definition, do not have the balls to initiate and pursue women." If you answer these questions sincerely and still want to date him, you then face the problem of making it happen - or rather, making him make it happen. They fall outside of the predator-prey model for sexual interactions that is assumed in the "don't initiate contact" rule.
The reason for this is that shy men are more concerned with avoiding the social catastrophe of asking you out and failing than they are of getting you.
So be careful about how much (and which) initiative you take.
Unfortunately there is no quantifiable or simple rule here, as his threshold for embarrassment will vary in proportion to his shyness and his pride, which are different in every man. Well, for starters, in the early stages, you will need to give him blatant signs of your interest.
Dating a shy man takes a lot of initial investment for an uncertain outcome.
You will probably get frustrated at his lack of response to your initiatives.