That was generally true in the Caracalla Therme
Home (the outdoor sauna shown post-dates my time) in Baden-Baden as well - the older and fatter, the skimpier the bikini. Bathing suits were required throughout, but were not permitted in the solarium upstairs, which included the saunas and a bar - I will never again have a beer before entering a 500C sauna. Guess who did and did not wrap themselves in towels.
There were a few delightful exceptions, though.