I don't think people have "rights" to service at a business. They have a right to make strange rules. You have the right to not use a certain bank. I think its pretty common for drive-through to not serve peds and bikers. I think the picture of the little guy banger his head on the wall is apt, you won't win the argument. So give it up.

If the bank doesn't service you at the window just take the bike inside, enjoy the A/C for a couple minutes, and take care of your business then leave. The key is not to ask, just go in with the bike.

PS If a guy with a gun tells you to leave with the bike, I would listen. Banks take themselves <sarcasm>very seriously</sarcasm>.