Swimsuits Parade, Sydney, Australia

In Classical antiquity swimming and bathing was done nude. There are Roman murals which show women playing sports and exercising wearing two-piece suits covering the areas around their breasts and hips in a fashion remarkably similar to a bikini of ca. 1960. However, there is no evidence that this was used for swimming. All classical pictures of swimming show nude swimmers.
In various cultural traditions one swims, if not in the nude, in a version in suitable material of a garment or undergarment commonly worn on land, e.g. a loincloth such as the Japanese man's fundoshi.
In the United Kingdom until the mid-19th century there was no law against nude swimming, with each town being free to make its own laws. For example, the Bath Corporation official bathing dress code of 1737 prescribed, for men:
It is Ordered Established and Decreed by this Corporation that no Male person above the age of ten years shall at any time go into any Bath or Baths within this City by day or by night without a Pair of Drawers and a Waistcoat on their bodies.