Examples of this abound in Victorian literature. Think about Jane Austen. How often does one of her characters decide to go for a drive or a ride by herself? If Elizabeth--or Emma or Anne or any of them--decides to go somewhere, she is accompanied by her mother, her sisters, or a friend. She does not announce, "It has occurred to me that I would much prefer to blow this joint than finish this needlepoint. Cheerio!" In fact, if she goes anywhere, it's generally just an excuse to get out of the house and it's within walking distance.
Or take a look at Thomas Hardy. In Tess of the d'Urbervilles, it is when Tess is walking home at night by herself that her true problems begin (though some might say it is really due to her complete lack of self-preservation). In The Return of the Native, Eustacia Vye roams the heath by herself, causing herself and the other characters no end of heartache. Each of these stories ends in tragedy and death.
There are probably hundreds of such examples of women's mobility serving as the "gateway" to sin, and so when the bicycle was introduced to England in the 1880s, it represented more than just one more form of transportation. It was easier and safer than riding a horse and less expensive than a carriage, and gave women a much wider range of activities and places to go. In addition, the bicycle serves as a symbol for independence, in part due to the fact that it is self-propelled; it is the rider's energy and strength alone that moves the bike, nothing else.
To this day, the bike represents an alternative way of life, free of dependence on oil and full of activity and fresh air--to most TV addicted, car-driving Americans, it's practically a subculture in the 21st century. There are still cycling events to protest Big Oil, the War, and even unsafe drivers. (The picture to the left documents the time last year my cousin was charged with indecent exposure for participating in the World Naked Bike Ride to protest the war. She's the one in the middle wearing a scarf and a tattoo, and she named her bike Naked--so she can ride Naked whenever she wants.)
Speaking as a bicyclist, or at least a non-car owner who owns a bike and occasionally rides it, my real sense of independence comes from being able to go the wrong way on one-way streets by just hopping up onto the sidewalk. Regardless, I have much more respect for the history of the bicycle than I did before I realized just what it might have meant to my grandmother's grandmother's grandmother.
For those who are interested in reading the article, here it is: http://www.cnn.com/2008/LIVING/wayoflife/05/20/women.bicycling/index.html