Not trying to create a new law here- I think it is already law that all wheeled vehicles, including bicycles, are not allowed on the beach. If I am wrong, then yes we do need to create a new law.
Bicycles on the beach IMO are even more of a threat to pedestrians and people in general than traffic on the road. You need to witness 20, 30, 40 kamikazee construction workers crashing through, over or around anything and everything in their way when they are riding on the beach.
As for bicycles on the beach in town, this has been for some time the most popular method of transportation for drug peddlers and now it is fast becoming the popular form of snatch/grab the purse, nap sack, fanny pack etc. and go. If keeping bicycles off the beach was fully enforced our beaches would be much safer.
Personally I would take Segways on the beach over bicycles on the beach. But the real answer is for all of us to work together to keep all wheeled vehicles off the beach.