Bank folders would be nice.
One folder per character with the one linked to your current character being of course selected by default.
This would allow easy transfer between characters.
Also, being able to move items within the bank would be welcome.
I don't understand why we have to first remove the item from the bank if we want to put it in a different slot. The current single click policy for the bank isn't all that helpfull.
This way, we would also be able to move the items directly to open backpacks.