Once you build a bank, it will produce money every few seconds. You do not need to supply it with gold or anything. It will only produce one piece of gold at a time though. There is a skill you can purchase that will allow you to generate more than one if there are multiple banks placed in the same area as each other. This will improve the total amount of gold you will get from a bank building.
Gold will generate in a bank, even when you are gone. If you decide to go and tackle a dungeon, the bank will keep generating money for you while you are away. Once you return, there will be a nice little nest egg of money sitting there waiting for you.
Is a Bank Worth Building?
A bank is quite useful and worth building but It shouldn’t be something you put at the top of your list. There are plenty of other ways to generate money in Forager and I would focus on these before spending the resources on a bank. If you have the resources to spare, then it is probably worth building a bank.