Bikes benefit a lot from pneumatic tyres, pressure pumps, smooth asphalt (not cobbles), precision engineering of chains, chemistry of oils and lubricants, rust-proof steel, rubber brake pads with compounds that last long enough and resist rain, spring steel for suspension, cables that don't stretch. Without those things you get a wooden boneshaker hobby-horse, large, heavy, energy inefficient, incovenient: https://duckduckgo.com/?q=hobby+horse+victorian+bike&t=ffab&...
(And internal combustion engines; how are you going to distribute them around the Roman Empire by the tens of millions without trucks or ships?)
(And internal combustion engines; how are you going to distribute them around the Roman Empire by the tens of millions without trucks or ships?)