Even if the bank branch is closed, they usually have private ATMs available that are much more capable than your average US-style ATM. You can do just about anything at those ATMs that you could do inside the branch.

At least, that's the way it was back in 2006, when my wife and I moved from Brussels, Belgium back to the US.

I remember many long hours sat at one of those ATMs (yes, they had private seating for most of them), paying various bills electronically using the bank account number given to us by the company that sent us the bill.