I am thinking of opening a new service called the BitBank!
Essentially, it is a 24/7 online "bank" for bitcoin services.
If we open, we will offer:
Physical Bitcoins in Paper "checks" or metal "coins"
Exchange from Money Order to BTC
A free lottery you can enter, where the jackpot is 1 BTC
Secure storage for your Physical bitcoins in our fireproof safes, free when you buy a physical BTC
And Some other custom services.
What "Banking" services will be offering? According to Wikipedia "A bank is a financial institution and a financial intermediary that accepts deposits and channels those deposits into lending activities, either directly or through capital markets. A bank connects customers that have capital deficits to customers with capital surpluses" (http://en.wikipedia.org/wiki/Bank). I have no idea how traditional banking services could be offered through Bitcoins.
What fees are you thinking of charging?