In most cases bank details are expressed within the payment terms section of the invoice. You can’t create custom payment terms for specific clients. Although when issuing a new invoice, if you copy from an existing one then the payment details will be translated to the new invoice.
There are also some feature threads requesting custom payment terms/notes per client (here’s one you may want to add your vote to).
We are also working on multiple trading style templates that may address this question too.