At the turn of the century this paranoia for safety and the segregation of genders eventually passed, however women were still expected to wear neck to toe dresses in the water. It was only due to the participation of women in serious swimming (as a sport) that their swimwear shrank gradually, starting with the reveal of arms in the early 1910s until the 1920s with the showing of legs (gasp!). It also seemed to be the tightness of the garment that caused outrage.
Vaudeville (and later, motion pictures) star and swimmer Annette Kellerman caused uproar with her risque swimwear. The Aussie "underwater ballerina" (a type of synchronized swimming which involves diving into glass tanks) first arrived in the United States in 1907, and brought with her a fashion revolution: the one piece swimsuit. Kellerman was even arrested for indecent exposure at Boston's Revere Beach in 1908, with the first outing of her "body stocking", and she soon altered the suit to cover arms and neck. The bathing suit allowed much more freedom than the layers of fabric previously worn, however it caused controversy by revealing the contours of the female figure. In some shocking cases, women even ROLLED THEIR STOCKINGS DOWN below the knees. Such a public nuisance were these women that the "Annette Kellerman" swimsuit was banned, and "beach censors" patrolled the sands handing out tickets and even collecting fines.
Luckily, women just kept on pushing for fashion-freedom and from then on, swimwear just kept getting smaller until we get into 80's thong territory. The first bikinis appeared just after WW2, named after Bikini Atoll, the site of several nuclear weapons tests - for their supposed explosive effect on the viewer.... get it?....