That offense will reflect negatively on you and the relationship.
So be careful about how much (and which) initiative you take.
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 whatever you would normally do to indicate your interest to a confident man, double or triple it for a shy man (in proportion to his shyness): While I don't suggest that you overtly ask out a shy guy on an "official" date (this would too flagrantly undermine what he knows to be his role as described above), I do suggest that you suggest and then ask him to hang out under casual pretenses.
A shy man may never become courageous enough to approach women in general, but he can eventually grow comfortable with a girlfriend or wife.
As the fear of the unknown dissipates with increased familiarity, a shy man's confidence in his interactions with you will rise.
His masculine instincts will kick in, and in some cases you can end up with a man that acts towards you the same way that a confident man would have acted from the outset.
So, if you do choose to initiate, do so only during the early stages of dating, that is, until he builds his confidence and comfort around you.