As others have mentioned, the resources to maintain bikes are not zero cost. Also, bikes rust in wetter areas fairly quickly if left outside/not maintained (your average chain is going to last ~ a year outside if not reoiled).
Bikes, mile per mile are more dangerous than walking, this might be because of cars etc, but with cracking roads and overgrowth, the risk to riding a bike becomes higher than walking. A single screw up on a bike is survivable in the modern world, it is less so in a post-apocalyptic one.
Bikes leave you vulnerable while travelling, you have to stick to main developed roads, you can only move so fast, you are easily taken out by a simple road trap. You have very little ability to 'take in surroundings' and you have to stop moving and abandon your bike to fight or hide. In a 'world gone mad' scenario someone on a bike moving overland is an easier target than someone on horse or on foot.
Bicyling long distances sucks a lot, especially for people who don't do it a lot. It's brutal on the body, hard to cross anything with elevation, and hurts the body in unique ways. Your average person might give up cycling fairly quickly for this reason. Horses, at least, travel with you when riding on them sucks.
Bikes don't work as well under non-ideal conditions. Heavy rain/snow/ice/elevation/heat all make bikes difficult to use or damage them.
Skateboards solve a lot of these (as they are easily portable). But the risk factor gets higher.
I'm not saying these items would be useless in a post-apocalyptic scenario. However, like most items, if someone wasn't extensively prepared to maintain and use them in a similar scenario, it's going to not work out for them except in the short term. (The same could be said about guns/cars/motorcycles).