A horse is a better alternative than a bike if you had a truly apocalyptic event. A horse can carry more and traverse terrain that a bike can't, plus it refuels on native vegetation. That being said, since the vast majority of people have access to a bike, I would think a carbon belt drive mountain bike with panniers would be the best option. Having a set-up for rainwater capture is critical, along with a stockpile of chlorine and a means of keeping the water in darkness. Two portable solar panels would be enough to recharge an ebike battery, or recharge a deep cycle battery that may be used to run a tv set. Aerial tv is a must. Who knows if the internet would be available, or even cell coverage.

We're pretty much sitting ducks for any long term disaster due to the complicated supply chain that exists, but if the dericho from a couple of years back taught us (at least us personally and our neighbors) anything, it was that "simple is better" and "always plan/stockpile for an extended disaster". A camp stove, a supply of nonperishable foods, usable on-site water, a sheltered place - this will get you through the worst, even for weeks.