Find a BB branch that is used to dealing with foreigners, e.g. Exchange Tower or EmQuartier. Their website has clear rules, maybe bring them with you:
"2. Foreigner with Long-stay or Tourist Visa
* Passport
* A Letter of Reference issued by: (One of the following)
* Embassy or international organization
* Customer’s home bank to Bangkok Bank via the SWIFT messaging network
* Person acceptable to Bangkok Bank e.g. branch officer, customer, government officer or company executive
* Educational institution located in Thailand and acceptable to the bank
* Company that is acceptable to the bank, confirming the customer is in the process of getting a work permit
In addition, other document that shows the name of the customer can be used as a supported document besides the documents mentioned above i.e. a document showing the ownership of real estate in Thailand such as a unit in a condominium."
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