I think you're comparing bicycles to an idealized version of horses. Real horses get tired quickly, get hurt easily, and are quite expensive. Assuming decent roads, a bicycle would often be more convenient, and almost always cheaper.
From Wikipedia: "A stagecoach traveled at an average speed of about 5 miles per hour".
> Assuming decent roads, a bicycle would often be more convenient, and almost always cheaper.
I think you're assuming an idealised version of roads. In all seriousness, good roads were usually cobblestones and bad roads rutted tracks until bicycle pioneers started lobbying for roads to be paved smoothly enough to make their then-expensive hobby more practical for transportation than horses and horse drawn vehicles. Asphalt and Portland cement roads were new technologies in the nineteenth century too.
From Wikipedia: "A stagecoach traveled at an average speed of about 5 miles per hour".
https://en.wikipedia.org/wiki/Stagecoach