Good question. It is also an interesting one since I'd assume this would stereotypically be the other way around. For starters, you have to realize that there's nothing wrong with your girlfriend. She's just not big on public displays of affection, and to the end, she's probably like most people who just don't like to fawn and fall all over their lovers in public. Some people believe that those behaviors are strictly for behind closed doors. There's nothing wrong with that.
The problem is that you are the opposite so you all need to find some sort of way to meet in the middle. Perhaps you can create some sort of subtle and discreet way of showing affection when you are out so you get the affection that you want and she gets the privacy she needs. It could be something as simple as a certain scratch of the hand or even holding hands under a table.
That kills two birds with one stone. My guess is that she'd probably like to be more affectionate she's just not comfortable with it. So maybe you can also make her more comfortable by putting your arm around her more or holding her more, in a way that doesn't draw attention from the couple engage in S&M acts down the street. That's usually the problem, the lack of discretion. If you put your arm around her, she can hold your hand or something and all will be right and well with the world.
It was written.