A woman could wear a bra and panties in public and would get arrested for indecent exposure, or prolly fined *I'm not sure really what the punishment would be*

BUT she could wear a bikini that is just as reveiling as the bra and panties, *and often times even MORE reveiling* and it's totally acceptable.

Why does it work this way?

I've seen some women who should have been locked up for wearing a bikini.

Basically the bikini was intended to be outerwear so society accepts it no matter how revealing it may be. A bra and panties on the other were not created to be outerwear (although you wouldn't be able to tell by the way a lot of young women dress these days!) so society does not accept them being worn in that way.