If you want to stay with Bangkok Bank try another branch, each one has their own understanding of the so call rules look at it as what Immigration does all the time.
This past two months been dealing with BB in Pattaya for a friend it is like pulling teeth even harder, one said need a residential letter, then week later manager acted as if they never heard of one before, but will do it but need to hold money in a time deposit, Then to another the one that actually got busted for illegally opening account for mainland Chinese as tourist why this all started!
Again, even with a residential certificate, refuse the rule as changed even when it hasn't this seem to be the common excuse, since my friend has lots of medical issue said go to doctor get a letter we can open one to use for his medical expenses.
So after a week, I was told given a small piece of paper go to this particular bank and give this guy the letter along with a 1000 baht, half hour later account opened, with residential letter, and passport,