No, you misunderstand.
The bank will have their own bitcoin wallet. When you deposit bitcoin with the bank, you transfer your coins through the normal bitcoin mechanism to the bank's bitcoin address.
The bank won't have an actual vault of bitcoins, their bitcoins will be stored on the distributed secure log like anyone else's bitcoins... but they will hold the private keys to their own wallet.
They will hold an account for you valued in bitcoins, but not actual bitcoins in the bitcoin log.
They will do this if they have to buy bitcoins themselves off of the exchanges... but they will offer incentives to you to store your bitcoins with them rather than in your own wallet, such as interest, security, having your employer pay them rather than you directly... stuff like that.
You can withdraw bitcoins to your own wallet if you want to spend them... they will transfer virtual bitcoins from your bank account, and the corresponding real bitcoins from their private wallet, to your private bitcoin address.
But from their own pool of bitcoins they can make loans that you will pay back in bitcoins with interest using fractional reserve lending methods.
Then the supply of virtual bitcoins can easily exceed the supply of real bitcoins, but their value will be almost exactly equal.
You think just because you can hold bitcoin yourself that there would be no use for banks... well, the same could be said about gold and currency too. You don't have to store your currency in a bank... but most people do... when bitcoin becomes mainstream don't expect the banks to just sit back and ignore it... there's bitcoins to be made for them too, just as they always have done with everything else.
The only difference is the government won't be able to print them new bitcoins if they run out. This was never possible when they held gold either. The technology changes, but the old methods will reamin.