(Pre) Historic Bicycle Technology

Possibly a silly question, but the people I've asked really haven't given answers that satisfied me yet.

Why wasn't the bicycle developed until the 19th century?

Vehicles with wooden wheels have been around just about forever (except in the Americas), so the concept of stringing a couple of wheels out onto a central structure isn't news. Mills and water clocks and other millennia-old devices have depended on the meshing of gears; using one small, powered rotating device to turn larger wheels should be comprehensible.

Sure, mass production would be difficult if not impossible, and the reliability factor isn't outstanding: wood can chip or break, metal can rust. But carts and carriages/chariots/coaches would be just as troublesome, and animals (or slaves) that propel them need to be fed and tended.

I'm looking at a "rational fantasy" in one of those the-magic-fades-away societies, where industry hasn't yet picked up the slack. The hero/ine is a young teen who is trying to catch up with a girlfriend who has been chosen to join the Queen's Corps in the imperial capital perhaps four hundred miles away.

The logistics of riding a horse would be too much for the story to handle. He's had to abandon the trade caravan that got him out of town because it'll be trading in the hinterlands for months before it gets where he's going, and meeting up with a more convenient one could take forever. Unauthorized movement between towns is frowned upon to the point where he can't take public transportation (horse-drawn coaches) without drawing the wrong kind of attention. Magic's not really an option, since what little of it is left is strictly in government hands.

I think that walking would take too long, though I may have to revisit that. But using a bicycle seems promising, if I can convince people that they're not totally out of place.

Eric