Inventions are generally dependent upon other inventions, techniques, and social conditions before they're brought about. For instance, we don't see steam engines until 18th century England because of metallurgy and deforestation. With that in mind, what were the various factors or necessary prerequisites for the invention of the bicycle?
The earliest bicycle type was known as "draisine", "hobby horse", "dandy horse" or "draisine". These were extremely primitive. The rider propelled the device by pushing against the ground with his feet. The frame and wheels were wooden, and there was a tiller-type steering mechanism. There would have to be some sort of bearing for the wheels and the steering head, and for reasons of size, I think this had to be metal.
Probably the societal conditions such as leisure time are more relevant here, but I'm not qualified to comment on that. You might get more of a response in /r/historicalwhatif.
The bicycle was wasn't invented in one day. It has evolved over time. It's popularity seems to have gone through cycles, with peaks in 1819, 1870s, 1890s and 1970s.
The draisine happened in 1817. It happened just after the crop failures of 1816, but it's unknown if that was related.
The pedals were added in 1860 and mass production was begun. This was just 10 years after the the Bessemer process dramatically reduced the cost of steel, and Whitworth's advances in precision machining were becoming widely known.
Dunlop's invention of the pneumatic tire in 1877 contributed to the 1890s boom.
Multiple speeds came with the Sturmey Archer internal geared hubs in 1903.
The Arab Oil Embargo contributed to the bike boom of the 1970s.
Sources: Archibald Sharp, Bicycles and Tricycles, 1903. David Herlihy, Bicycle: The History
