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.
Of course, he will question this over and over in his mind, wondering whether you were asking him to hang out just to be friends, or if you wanted something more.
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.