Public is the opposite of private. Its definition varies depending on usage.
in the public would mean amongst people who are not necessarily friends or acquaintances.
No one I know uses it as a shorthand for pube licking, but it could. And it could also stand for a smelly person named blic (P-U-blic)
Cilbup is public spelled backwards and has no meaning whatsoever.
Anagrams of Public: Club Pi, Cub Lip, Lib Cup. If you are partying at Club Pi with mathematicians, you are unlikely to be in public. Libertines and women libbers seldom wear cups.