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.
In my opinion, the attention he pays to you when you are alone with him is more important and much more significant than his public display of affection. It is certainly more romantic and intimate to be able to express how you feel about one another when the two of you are alone together than doing it while others are around watching you. So much of the time, PDA is more about putting on a show for someone else than expressing how much he cares for you. It becomes a way of showing ownership, of one person possessing another. It is kind of an in-your-face way of saying, "This is my girlfriend and everyone else better stay away from her." It becomes a way for a guy to "mark his territory," so to speak. If he is affectionate enough to you in private, and obviously you're the only one who knows whether he is or not, why should it be necessary for others to know about it?
Maybe he is a grown up and more mature than you
I know a guy who won't touch his g.f at all in public.. isn't that nice!! hahahahaahaha.. that is pure love right there.
It's the opposite for me. I'm really shy and often have issues with showing affection if we're in public, but my boyfriend respects that and swears he's perfectly fine with the way I treat him.
I know of a guy who compares hand-holding to anal sex...... he doesn't wanna be pressured into it!:)
People have different comfort levels, you just have to accept that. It's not personal.
My relationship went from him never showing me any affection when anyone else was around to being obsessively clingy.