Online dating for the shy
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.
As the fear of the unknown dissipates with increased familiarity, a shy man's confidence in his interactions with you will rise.
If you are looking for an abundance of devotion, he has it to give.
So, in conclusion, if you are interested in a shy man, start by questioning that feeling.
Once this happens, you will need to gradually assume a less assertive (more traditionally female) role, because he will then be more liable to get bored with you, wonder if he could do better, consider his other options (the perception of which his newly-found confidence will likely inflate), fool around, etc.
The second caveat is that even a shy man has pride.
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.