Can you think of a fairytale with a bicycle in it?

This is an interesting one.

Basically your problem is that most fairy tales are old - mostly they proceed the modern era of the bicycle. The Victorian era of pennyfarthings seems to fit with fairy tales from our perspective nowadays... Even some tales from the 19th Century like Dickens or Peter Pan wouldn't include the bicycle because at the time it was seen as a very modern (not nostalgic or romantic) and symbolic of industrial and social change, just like trains were then. The bicycle had a huge role in changing the relationship of the sexes and The Rational Dress Society. Also it was one of the first consumer items and really impacted the world by changing mobility.

I got some interesting pictures when I did a Google image search. Basically, you are going to only find modern sort of post-modern nostalgia stories that combine the modern bike with old world magic. Unless there is a Disney movie with a bike in it that I can't think of (and I should know) you're not going to find anything that resonates popularly. Hayao Miyazaki, the Japanese Disney (except much, much better I'd say) uses bikes quite a bit. But never as the focus that I can think of. The best bike animation i can think of is obviously Triplets of Belleville. It is great and people would recognize references to that even though it is modern. But not really PennyFarthing era. The most fairy-tale movie story of biking I can think of is Breaking Away, but that also wouldn't fit.

I'll have a look in my copy of Bike Cult when I dig it up. If anyone would know it (other than Google), that book would.

Some friends of mine did the Rocky Terror Dino Opera which was a combination of the Dinosaurs Against Fossil Fuels and the Rocky Horror Picture Show... The Pedal Powered bikesexual Goddess turns the milky way in her thighs. But that would be a little weird and off topic to answer your question... and that wouldn't be recognizable to anyone unless you went to the Fringe Festival here in Vancouver.

Maybe something old and victorian with a frog in old fashioned get-up riding a penny farthing seems to ring a bell but I can't place it.

Wallace and Grommet?

You may have to improvise or hybridize something. You could personify the bicycle.

Or just do an animal or magical creature riding the bike. Alice in Wonderland?

Oh yes, The Third Policeman. There's a classic story with bike in it. Pretty weird also I'm afraid.

Animals. You can't go wrong with animals.

most the disney films have pennyfarthings in could be anything.