Credit: Andrew Ritchie http://andrewritchie.wordpress.com/2010/01/16/the-wheelwoman-search-for-copies/The other thing that goes around is fashion. It appears that the current debate over appropriate cycling attire has changed little since bicycles became popular in the 1890s. At this time, women's clothing was still very restrictive - floor length dresses, corsets, lots of drapery and puffed fabric. When women started to ride the bicycle, things changed rapidly. Bloomers were introduced to the horror of many refined Americans. Short skirts (as in knee-length), knickerbockers (as in knickers or pants), and even early skorts (split skirts with a panel that hid the split) started to become acceptable in public. Doctors, who had long disapproved of corsets due to their health effects, strongly discouraged their use in cycling and other forms of activity. In fact, doctors and feminists joined forces to promote the new women's fashions. The following article is by a physician, reportedly published in "The Outlook" in April, 1896 (I don't have the original). Click to view larger.
There are many, many similar articles about "wheeling" closthes for women...from the US, England, New Zealand, etc. A few more interesting links: an article on How to Ride the Bicycle and What to Wear by Mary Sargent Hopkins, and a seasonal article in the 1897 Brooklyn Eagle.
Disclaimer: To the best of my knowledge there is no copyright or other infringement for me to post these for non-commercial purposes.