If you have FCOIS, disable or remove it. That has fixed the problem completely for me.
Failing that, if you really really must have FCOIS active, open the inventory screen (!) before attempting to interact with the bank. This lets me withdraw and DEPOSIT items without UI errors most of the time.
In general, addons that change the way the inventory is displayed are to blame here.
FCOIS is one of the known culprits, something about it causes other addons to break.
But there are probably other addons that cause such conflicts, best to try disabling them one by one and see if that helps.
(edit:typos)