Does anyone know how much a Thai bank charges for a notarized document, such as a Power of Attorney? Does being a customer of the bank receive a discount?

Never heard of a Thai bank offering notary service like in the West, usually hear about lawyers or accounting firms providing that service 

If for use in Thailand there are lawyers who have special authorization to act a notary - but Thailand has not signed on to international agreement yet so such signatures might not hold up in court outside Thailand.  Believe many Foreign Consulates can provide such service for documents to be used in their country (know USA does).