Bank accounts, or any accounts or registration or identification whatsoever, are by No means connected to Bitcoin in any way.
The "connected to bank account" stuff is only where fiat money ($ or €) is involved.
Reason you can't pay with credit card (which is also connected to your bank account by the way) is that credit card payments can be reversed even months after the purchase, whereas Bitcoin transactions cannot. Same problem with paypal. This makes credit cards and paypal extremely risky payment options for merchants or sellers.
The usual procedure is: you buy bitcoins online, usually by sending $ or € to an exchange, convert it to ฿ (at this point it's still in some account at the exchange that's connected to you). Get the ฿ out (to your own wallet), mix it through some other wallets if you're really paranoid (really not necessary, just saying) and now nothing is connected to those bitcoins at all.
One of these will probably be both available to you and anonymous. https://en.bitcoin.it/wiki/Buying_Bitcoins_(the_newbie_version)
– Nick ODell – 2014-10-13T21:30:50.820Try local bitcoins. They allow you to find someone in your area and you can buy with cash (but you will pay a ~10% premium for this). – Tyler – 2014-10-13T22:12:17.690