While at the bank (and the bank window open), you would be able to right click an item in your inventory and send it straight to the bank (instead of getting property options for that item i.e. use, equip, info).
When the bank window is not open then the normal functionality menu returns.
Similarly, right click on items in the bank window sends them to Inventory.
In its current state, the method is very cumbersome, drag and drop, drag and drop.