The only way I know that you can transfer bitcoin without the internet is with a physical device such as an Opendime or this new SatsCard product that is being released. Both are by CoinKite but they both require a certain level of trust.
Opendimes aren't wallets that can transfer bitcoins in and out. They are physical USB-looking paper wallets. You generate its private key yourself by copying random files to it to provide enough entropy. That's the difference between an Opendime and a physical coin whose creator could have made a backup of its private key. There is no backup to make with the Opendime since the key is created locally on your side when you want to use it. That's the theory, at least. I am not aware of any known bugs where people have lost their coins that would suggest that someone else might have known the private key, unless it's a user mistake of course.
When you hand someone an Opendime, you can't consider that a transaction has occurred and say that it did without the use of internet. It's the same as giving someone a piece of paper where there is an address or a QR code and a private key. There was no transaction. You just gave someone a funded address and a way to reveal the private key of that address that allows the person to spend the coins. When that person wants to spend their BTC, an on-chain transaction needs to be broadcasted using the revealed private key.