I think you should use ur bank account to verify it first....You can check ur account for more details..
your account does not need to be verified in order to get a bank withdrawal, however you wont be able to withdraw more then few bucks on first withdrawl they will send u a special code in your first swift transfer which you need to provide them in order to get verified then you can withdraw big amounts
Its better to get verified via address first which will take 2 to 5 w0rking days and then you can add your bank account after adding swift code and it will not take much time too and you will be able to withdraw funds without having any issues ...
I think that they have to verify the bank first, since that is where they will be sending your money to, right? I have not used MoneyBookers myself, but some of my friends have in the past, I only use paypal.
its easy, first verify with the address, then add your bank account using swift code. then you'll be able to withdraw fund o your account.