First There Was Wool

 First there was Wool

Prior to the middle of the twentieth century, bathing suits were typically constructed of wool or cotton.
Until rayon was introduced in the 1920s, the main available fabrics were linen, cotton, silk and wool.
Wool was considered a suitably durable material for swimsuits because of its resistance to wear and tear
and its resilience against dirt. According to an advertisement for a mohair bathing suit found in the 1908 Sears,
Roebuck Catalogue, wool was an ideal fabric for bathing costumes as it “…sheds water well and does not cling to the figure”. 

The Miracle Fiber - Lastex
About 1925, an elastic, two-way stretch textile made from Latex was introduced, called Lastex.
Lastex is a yarn that has an elastic core wound around with cotton or silk or nylon or rayon threads.
Lastex was registered as a trademark in 1931. Lastex was know as the 'miracle fiber' when it first came out.

Lastex fabrics can be made to stretch one way or two, or all ways, depending on whether the elastic thread is used only in the warp, or in both warp and weft, or in a net. There are many different Lastex fabrics –for example, batiste lastex, satin lastex, lace lastex, and a leno lastex which, though extremely strong, is very light in weight, and so is much in use for garments designed for tropical wear.

Lastex began to be used in swimwear starting in the late 30's and continuing through the very early 60's.
The smooth fitting and flattering fabric allowed swimwear and foundation  makers to produce products
that enhanced the figure, were lightweight, and fit snugly. Mabs of California, Cole, Catalina & Jantzen
were some of the first companies to use Lastex in their swimsuits. Cole went so far as to patent thier own version of Lastex called Matletex.

And Finally Nylon
Nylon's advent created a revolution in the fiber industry. Rayon and acetate had been derived from plant cellulose, but nylon was synthesized completely from petrochemicals. It established the basis for the ensuing discovery of an entire new world of manufactured fibers. DuPont began commercial production of nylon in 1939.
And then there was the war, which had most nylon manufacturing go towards Military supplies.