Bitcoin is almost impossible to steal, and it would be much more expensive to attempt to find private keys than it would to just mine it. Your credit card info got stolen, not your bitcoin.
They need more than only your credit card. Bitcoin Exchanges are regulated as money service businesses and are required to know their customer, which means they have to do some basic identity validation. So the thief would need to steal your identity. This could be your exchange password at Coinbase or some other exchange. Always use two factor authentication on your financial accounts if its offered! But yeah, if someone does an instant buy of Bitcoin and sends it somewhere... it's up to you to seek indemnity from the bank by reporting the transaction as fraud and that person is $500 richer. It'd be hard to find the fraudster but not impossible.
