Some women can have orgasms doing the most mundane of tasks... some can even get off just by thinking about sex or exercising the appropriate muscles. Thus it stands to reason that theoretically a woman could have an orgasm while cycling.
But does it actually happen? Somehow I doubt it. Or if it does its extremely rare.
Let me take one proven urban myth as an example... Fan Death.
Fan Death is a superstition in South Korea wherein if you have a fan running in your room while you sleep at night and there is no window or door open, you will die from either asphixation or hypothermia.
This urban myth / superstition is so widely believed of in South Korea that all fans must be sold with a timer which automatically shuts it off and the South Korean government actively warns its citizens about the dangers of fan death. (All fans sold in Korea must be sold with a sticker on it warning them of the dangers of Fan Death.)
Koreans are so obsessed with fan death they've even come with a number of theories to explain the myth. ie. The fan creates a vortex which causes all the oxygen in the air to be sucked in together, depriving the person of needed oxygen. Other theories suggest the fan uses up all the oxygen or that it "chops up the oxygen".
Whenever South Korean police find a dead person in their bed and they can't determine the cause of death... they look to the fan. The fan is to blame. Thus the South Korean government has statistics showing the number of so-called "fan deaths" that have occurred because they never bother to do an autopsy and determine the real cause of death. (ie. the wife poisoned their tea)
Sounds ridiculous right? Foreigners to the country are rather mystified/amused by the fan death superstition because frankly its so mindbogglingly stupid its amazing anyone would be dumb enough to believe in it.
And yet many Koreans do believe in fan death, mostly because they've been raised with it and shown lots of statistics of dead people in their beds showing it does exist.
Its a bit like people being raised and told that their god exists. As long as nobody bothers to shatter that nice little illusion they will keep on believing in the idea because all the evidence they've been shown suggests its real. They're not about to question the validity of something when everything they've been shown or told suggests their god is real.
Thus, back to bicycle orgasms, as men we've been shown a lot about women anatomy, orgasms and what not... there's a lot of prevailing sexual mythology out there which may or may not be correct or completely false. We really don't have a clue. We are raised and told that women can be stimulated by almost anything between their legs so from our perspective it must be correct.
We can even come up with statistics for women who apparently can have orgasms while jogging, sitting on the subway or sitting on the clothes dryer... we have no idea if its even true, it could just be women bragging and pretending that they can to see if anyone will believe it, thus creating their own little myth.
(Its no wonder a lot of men think the G-spot is an urban myth... there's so much mythology surrounding it.)
So can a woman have an orgasm on a bicycle? Maybe. But can you prove it?