To be more frankly and conservative, people would rather barter needs like water, food, clothes than gold/bitcoin. Until that Zombie apocalypse were done and the whole world will be rebuild again but as one nation or few nations, maybe there will be a consideration wether the currency would be gold or bitcoin.
Could apocalyptic culture be based around Bitcoin though?
Communities could have their own maths guys mining bitcoin by hand.
These communities would have to be situated a geographical distance apart.
Transactions would be carried on paper by messengers on horseback.
Once a year, the blockchain commisars from individual countries could convene somewhere like Switzerland and sync the blockchain.