I offered more for this bank property than the buyer who got it.

Sorry to hear that. There can be many reasons why a seller picked someone else. A very common answer is the other person might have been paying cash and could close faster than someone getting a loan. I offer home mortgage loans in WI, MN, IA, ND, SD. Find me at Wi-MortgageBroker.com - Cambria Mortgage, NMLS 274132

There may have been other components on their offer that was stronger than your offer ...price isnt always the driving factor ....( eg. faster closing ..non refundable Earnest money deposit ....larger down payment ...cash offer versus needing finanacing etc ....)