Actually, women wore fashionable cycling "bloomers", not skirts. Reason for the "ladies" bike design was because it was "unseemly" (read this as "sexually suggestive") for a woman to "throw a leg over" a horse - which is why women rode sidesaddle - and that followed through to the mounting of bikes as well. Thus the step through was born (ie: to discourage a gentlemen from get all hot and bothered seeing a lady mount up.)

And now you know.