I need to weight-in here as someone who cycles a lot. Bicycles are surpisingly complex. they have collared bearing's, cranks, brakes and gears. Bearings alone require a degree of industry to produce. The other issue is roads. According to the common narrative, modern roads (macadamised+) were developed alongside bicycles and for bicycles.
It would be pointless to build a bicycle or 'bicycle shaped object' if it was simply easier to walk or ride a horse. However, as many here suspect, technologies sometimes come and go and people tend to underestimate the ingenuity of the past. Those little e-scooters being very similar to the little Velocopeds of the 1920's comes to mind.
So, even taking into consideration the complexity of cycling and its infrastructure, I still have a suspicion that something similar to the modern bicycle may have existed at some point in history with civilisations that where capable road builders.
(On a side note, I would like to hear some discussion on 19th century road composition, oddly specific, but if you want to understand a civilisation, you have to know what it's walking on.)