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.
Curious about the "semper ubi sub ubi"? It's silly Latin that Latin students like to say since it comes out sounding like "always wear underwear" if you translate the individual words in sequence. Semper can mean "always", ubi can mean "where" and sub can mean "under".