Bank can trusted but as for bitcoin is one currency that can not be trusted with the bank because they can always have their way in control of it so i really can not trust the bank over some a month of money but i trust bitcoin over all transaction of money it is fast and is very easy anywhere you can do your transaction
Bitcoin is not related to banks at all, banks has nothing to do with bitcoins, there is not banking system that asks you to deposit your bitcoins there if you have, they can never insist you on this even if they have any services like this because they wont come to know about your bitcoin possessions.
Bitcoin and banks have difference in usage, but banks are the traditional finance management supporters. Without banking system we might be living back to some ages of civilization. Now as a alternate based upon requirement digital currencies have evolved for which we should not have a negative trust upon banking.