Benignuman,
A woman has to cover her hair in public even if that public consists entirely of other women, and even if she lives in a society where it is the norm to walk around with uncovered hair.
Any normally covered part needs to be covered, even in the exclusive company of women. I know of no way in which covering hair is more chamur than the areas that need to be covered even before marriage.
My knowledge of how frum women conduct themselves at pools comes entirely from reports from my wife.
I wasn’t c”v insinuating otherwise.