It has been a few years ago that I used their Baht Remittance Service. It took about 11 days from the time I sent money from my USA bank to Bangkok Bank's NY Branch and it arriving in my Bangkok Bank account in Thailand. The process:
1 Downloaded the Application which is a pdf form, completed it, and emailed it to the NY Branch along with the Identity page from my passport. [link for doing the download is on their webpage https://www.bangkokbank.com/en/Personal/Other-Services/Transfers/Transferring-Into-Thailand/Foreign-Remittance
2. Using my USA bank on line banking, I ordered a check* payable to the NY Branch and had it sent by snail mail to the NY Branch's address.
3. The NY Branch after depositing the paper check, waited for it to clear.
4. The NY Branch then converted the dollars to baht** and transferred it to my Bangkok Bank account here in Thailand.
5. Although they remitted the money to me based on the emailed application, at the time I used the service, they required the original be sent to them by snail mail and if not sent, they would not not process any future transfers. [In looking at their current information, that appears to no longer be a requirement, but that may have been in info I received confirming approval of the application]
* Personal checks mailed to them are not acceptable, but they will accept it as a bank money order if sent by your bank [I confirmed by email with them beforehand that they would accept my USA bank's issued paper check] - see Item 11 under Terms and Conditions which are on the 2nd page of the Application Form.
** They will send US dollars if requested, but according to their website, the fee will be $55 [IMO unnecessary unless being sent to a US Dollar account rather than a baht account - when I did my transfer, unlike US banks, the exchange rate used by the NY Branch was the same as used by their HQ here in Thailand.