I've dated countless women and it has always amazed me how little they know about men.
If nothing else, this blog is an outlet for voicing my astonishment at the typical female's ignorance of the male mindset.
That offense will reflect negatively on you and the relationship.
The first thing to do when you find yourself attracted to a shy man is to question your feelings for him.
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.
You will probably get frustrated at his lack of response to your initiatives.
The biggest problem is that it won't be clear to you whether or not his unresponsiveness is a product of his shyness or his lack of interest in you - because it could be either one. His persistent willingness to hang out with you might be stem from a real interest, but it also might be a manifestation of his unfulfilled desire for female attention; he could just enjoy dabbling in the idea of a relationship but at the same time not like you enough to want anything serious with you.
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.
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.
Aside from their innate male tendency to overlook anything that isn't spelled out in black and white, shy men will by default doubt any sign of your affection.
At most, it is a reliable source of advice for women who want to improve their chances with the opposite sex.
A post I made about why women shouldn't take the initiative in relationships evoked some questions about how to deal with shy men - after all, shy men don't chase women, and are unlikely to initiate anything.
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.