Why? If the guy is shy and not comfortable with a lot of public affection, why push him to do something he doesn’t want to do?
If homey refused to touch you at all in public, I’d see your side of it, but that doesn’t sound like the case. If he’s doing the basics — hand-holding, an arm around you or the occasional kiss — isn’t that enough? To me, PDA is like wasabi: a little goes a long way. Do you enjoy watching strangers eat each other’s faces in the movie theater and rub each other’s asses on the sidewalk? I don’t — I want to turn a water hose on them. Some things should be private.
Maybe your goal isn’t harder-core affection, but affection more often, which is fine. You can encourage him by letting him know you like what he’s doing whenever he touches or kisses you. Positive reinforcement is never a bad thing, and it works.
I can’t help but wonder, though, if there’s more to this than just affection. Could it be that you have a need for the relationship to be validated in public? Do you want more PDA because you like it, or because you want people to see him being affectionate to you? I wonder the same thing when people complain about their partners not validating their relationship on Facebook. Does it really matter, or are you that insecure about your relationship?
Maybe you are, maybe you aren’t, but it’s a question worth asking yourself. Beyond that, try positive reinforcement and don’t push too hard. Give Shy Guy some time and space and I bet he’ll warm up to the idea of being more demonstrative in public.