If you both have full node bitcoin wallets it's possible, just like how it worked in the first place. But having a full node on your computer takes up >350GB of space now, so I doubt there's too many people that still do that.
Is this true? You still need connections to the rest of the network so that you know your block chain is the longest one and you get the number of confirmations that both of you feel is sufficient to remove double-spend risk. So it's not really just between the two of you, even if you both have full nodes. Right?
Crypto-currencies don't provide a way to transfer value peer-to-peer, online, just a third party that is (hopefully) neutral.