In general you will need youer passport with a visa stamp, but which visa is not everywhere the same. Best is a 3-month visa. Then you might need your rental contract, and that should be all. Careful: each bank and each branch has slightly different requirements and from my experience it is easiest in tourism areas. Good luck.
P.S: If you have a Thai to come along (NOT a bargirl!) that should help.
Get the right documents and then try different bank branches until you find one, that accepts you. A bit time consuming, but you can do it on your own.