I have seen so many times in news stories that bitcoin mining reveals a series of new bit that make up a bitcoin, or that a bitcoin is just a series of bits.
Bitcoin is a ledger, that ledger is public. The columns are labelled with things like 17Zsi2TiKrZoAoaQ7bzt3wPB5NZV1T4KeE, That column _is_ the bitcoin in your wallet. You need to have a password to move something out of your column and into another. That's the private key to your wallet.
Most people understand ledgers. Most of the misunderstandings about bitcoin (especially regarding anonymity) indicate that people don't realise that bitcoin is a ledger.