I tend to agree, 100yr is a bit early.
That said, there may be alternatives to steel wire spokes (tho IDK if they're exactly practical). In the same way wire replaced whalebone, couldn't whalebone be used?
Could liberal application of whale oil (or some form of grease) substitute for ball bearings?
The big technical innovation necessary is the chain drive & drive sprocket; could that be by belt drive? (That seems to require development of mechanisms to produce rotary motion, & IDK how early those were.)
Given you get a "perfect storm" of innovation, tho, the bicycle does drive developments in better roads. It improves opportunities for travelling salesmen. It offers opportunities for travelling tradesmen/women (seamstresses could deliver, frex). It improves medical care (doctors could travel more readily, & would be the #1 market, as for early cars). It increases tourism. It sparks a degree of "gender mobility", as women can use them to do things they couldn't before (tho this has been exaggerated). It creates opportunities for standardized manufacturing (which was commonplace in the bicycle industry long before Ford came along). It sparks demand for new technology (like wire spokes...with spinoffs elsewhere, like in umbrellas). And it creates whole new sports (velodrome racing, bicycle road racing).
All of these are OTL events. I see no reason they'd change if they happened sooner. The only issue is, are the bicycles themselves good enough to allow them, or so bad they prohibit.