The top is a band, probably a long piece of cotton or linen cloth wrapped around the breasts, rather than an actual bikini top. It is called a strophium. There are other possible names for it: fascia, fasciola, taenia, and mamillare. Its purpose was to hold the breasts and may also have been to compress them. The breast band was a normal item in a woman's underwear. The same can not be said of the "bikini" bottom. The bottom loincloth-like piece is probably a subligar. A male athlete might wear a subligaculum. There may be no difference. The subligar/subligaculum was worn by athletes, slaves, and certain others, but was not a normal element of underwear, so far as we know. That is: the normal clothing included under tunics and breast bands, but not underpants/drawers/briefs.
Whatever else, it is interesting to see the possibly idealized depiction of the shapes of the Roman women, with their firm, probably well-muscled legs and arms, broad hips, and small feet.
See: "Roman Underwear Revisited," by Kelly Olson. The Classical World, Vol. 96, No. 2 (Winter, 2003), pp. 201-210.


