At some point, the fridge logic sets in and viewers start wondering just what's wrong with post-apocalyptic humanity for them to completely ignore the world's most popular form of mechanical transportation. Heck, bikes at the very least are silent. An engine in a depopulated world would surely be heard from miles away. They don't even keep one in the trunk for when/if their car breaks down or are low on fuel.
This can be somewhat justified if it's more than a few decades After the End, because roads would break down and become overgrown, which Jeeps and such could handle, but non-mountain bikes couldn't. In fact, a movement for "good roads" (i.e. any paving at all) began mostly on the insistence of cyclists in the late 19th century, only later getting taken over by motorists, and the first prototype of a mountain bike only appeared in the late seventies.
For a little history: the forerunner of the bicycle was the draisinne or hobby/dandy horse, which was just two wheels with a steering mechanism and no pedals, so the rider had to push the ground to propel it+ ; it was made out of wood and lubricated with animal fat. The first model with pedals, the velocipede (popularly known as "boneshaker", as it had no vibration dampening whatsoever, not even tires, which came later) was built in 1839 by a blacksmith. As such, there's really no reason (aside from tropes being tools) that a post-apocalyptic world couldn't maintain or manufacture their own basic bikes. They might not be as complicated or as comfortable as modern bikes, but they'd still get you places without having to worry about fuel or animal care, and still be relatively fast at it – even the draisinne can glide easily once it picks up enough speed.
Now, if the ancient technology is randomly picked at and put together improperly, you've got yourself a Scavenger World, and it might at least make a bit of sense not to have too many bikes. That's at least a bit excusable. But if you're watching or reading a story where gas-powered vehicles exist and foot-powered ones mysteriously don't, then there are No Bikes In The Apocalypse.
So why do writers have their characters do this? First off, they (correctly) believe most people like cars and trucks, and want to live vicariously through the characters. Secondly, the very reasons why having a motor vehicle is a bad idea in real life are why it's helpful for writers: you can instantly add drama by having the vehicles break down, run out of fuel, or be stuck inside while the zombie hordes/mutants/creatures/bandits try to get at them. Lastly there is the motive of cash - a TV show or movie simply can't ignore the money Product Placement gives the production, and car companies give a LOT of money.
Another factor is the culture where many of these works are created: Hollywood. Hollywood is within the Los Angeles Metropolitan Area, where bicycles are notoriously impractical due to the large distances one has to travel (such that only motorized transport is practical), the lack of bicycle infrastructure, and hostility of motorists to bicyclists making it dangerous to ride a bicycle around Los Angeles. The result is that many of these writers rarely even think about bicycles, let alone use bicycles themselves, or, as motorists, they view bicyclists as obnoxious obstacles. They are simply employing Write What You Know, and if they don't know how to ride a bicycle, or they don't like bicycles, they won't use bicycles in their works.
However, you should be careful not to overlook the fact that no matter how good a bicycle is, it's not a car. A bike can't carry more weight than can be propelled by the muscle power of its rider, can't carry more than one person over long distances unless specifically adapted to it, provides no shelter from rain, bullets, or the claws of nasty critters, and unless you get a long downward slope in your path, you can't really rest while riding, since the rider is what powers the bike. In Real Life, many who are into "prepping" debate the intelligence of keeping a bike as a primary means of transportationnote in the event of catastrophe, namely because the bike doesn't provide the protection of a motor vehicle, is nowhere near as fast as a motor vehicle, but like a motor vehicle it can paint a huge target on the back of the owner in the eyes of other (possibly hostile) survivors unless its silent operation is taken full advantage of. Of course, gasoline goes bad after a year or so (so no, you can't stockpile enough of it) and in countries such as The Netherlands or Denmark there are more bikes than people, so while people might steal good bikes, anybody stealing a bike if they're literally just sitting on the street stretches belief. Turning murderously violent over something like a bike would just seem silly if you can take a decent cruiser off the countless corpses in Amsterdam or Portland, or abandoned department stores in most countries* .
