You seem to be looking at this the wrong way. All laws are (supposedly) based on intent. I carry into my bank regularly and do not need to ask anyone if I am allowed to carry into the bank because I am breaking no laws and my intent is lawful business at the bank, therefor it is unequivocally not any of the banks business if I have a weapon on me.
The way I see it, carrying to the bank is for to the front door, and away from the front door. If I'm in a bank while it gets robbed, I doubt I would engage them and let the bank handle it. I assume they have insurance for those things. The gun is for the walk back to my car, which is probably not the banks responsibility . To ask permission is to un-necessarily muddle up the situation and make waves. If you walk with honor and Lawful intent, there are very few places that you can not carry.
I think storing a weapon in a safe deposit box is a dandy idea. Remember, you pay for having that lock box in the bank. Think about that for a moment and tell me what that is! You are buying secure privacy. You paid for that box, now you have the right to an expectation of privacy surrounding the contents of the box. It is now none of their beeswax.
