I would say that what you are suggesting is one of the riskiest ways to hook up, and most couples on here wouldn't dare.
In nearly all countries sexual activity on a beach is illegal, so you are asking her to jump from not playing around to doing something which could lead to her being publicly disgraced and even going to prison. That's a big jump!
If you really wanted to do this then look up Cap D'Agde in France. It is a nude seaside town with lots of swingers clubs where sexual activity in public is ignored by the authorities. Or if you are in the States then somewhere like Hedonism might be more accessible.
But if she agreed to go to either of those, then she would probably agree to go to a Swinger's Club or for you to post photos here and for her to join in with finding someone through this site.
I don't want to crush your fantasy, but feel that you are asking waaaay to much of your girlfriend and gentler steps might lead to more fun!