As Mishna B'rura 2:1 notes, one can bathe in a river or go to a bathhouse dressed in whatever clothes are normal for doing so, even if that means no clothes at all, so long as one is clothed until he gets near the water (as near as feasible) — this, despite the general idea (Shulchan Aruch 2:2 there) that one should be dressed even when alone.
Besides 2:2, the only halacha-based reason for a woman to avoid exposure of any part of her body (besides oso makom) that I've heard of is so that men not see it. (But I'm far from being an expert.)
A girl I know went recently to a women-and-girls-only swim (where even the lifeguards were guaranteed to be women). She reports that a number of religious Jewish women and girls swam in garments that covered large portions of their bodies not normally covered by swimmers: specifically, most of each leg and most of each arm. Does anyone know why they might have done so? In particular, is there any halachic basis for doing so? Any musar-type basis?