The banking service of the Agnes really considers it when you've got so rich that your backpack is brimming over. The Bank Manager could be found in the Maincities.
Talk to him to activate the bank interface, which is made up of the bank sector on the left and backpack sector on the right. There're 2 pages within the interface.
Click on or drag the item you want the want to save for you, it would move from the backpack side to the bank side.
Items of the same type could be piled up by dragging them along in the bank.