Bikes in D&D? :blink:
That's an . . . odd idea. I could, perhaps, see one or two in a gnomish settlement - itself in the middle of a large gnomish nation that is relatively advanced. What's that island in Faerun, Landun or something like that? Perhaps in one of the cities there. It would be as rare and exotic as fire arms. Possible, but quite unlikely. Not at all used by adventurers, I would think, due to the ease of breaking, the scarsity of spare parts with which to fix it, and the fact that it cannot handle some terrains as well as a horse might be able to do so (such as open field, most forms of rough terrain, steep trails along escarpments, etc. This doesn't even take into account that the wheels would be solid wood or metal.
Personally, I think it would be better to introduce the horse drawn carriage. I seem to recall an (older) fantasy series that I came across in a library one day. Its entire premise focused around an individual in a low magic / late middle ages fantasy world (just about to enter the renaissance, so think around the early 1300s) who first developed the horse drawn carriage - and his latter attempts to start the equivalent of a busing line for elite customers between two major cities (ie: 2-6 wealthy individuals taken from one city to the other in a horse drawn carriage). Its been ages since I read those books. I wish I could recall the titles or the author. It was only 2-4 books long, that series. Ah, well.