Or internet access. It seems like you could commit fraud by traveling to regions without a means to communicate with one-another online and selling them BTCs that were already spent on another network.
I bet two people pull that off before those communities ban BTC.
On the other hand, as long as those communication islands don't reconnect, all those double-spent BTC will be just as good/bad as homemade dollar bills.
Bitcoin might be postapocalyptically valuable if the apocalypse in question has hyperinflation at its core, but in a scenario without that it will be inferior even to vintage paper money. The true availability of BTC within a given community is just too much of an uncertainty. What could be a sizable fraction of the amount in active circulation one day could be completely devalued due some early adopter backup going live a day later.
I bet two people pull that off before those communities ban BTC.