Anonymous participant it took about half a week, this was late last year. I'm sure they're much more busy now and probably take a week. Is your school going to give you the docs to do it yourself or give to an their partner agency to do it. Either way, I recommend getting a copy in case if immigration ever asks you for them when you try to enter the country (slim chance but you never know)
Myself and a group of friends got approved with Bangkok Thai Cooking Academy, we all did it ourselves. From memory I submitted receipt of the course, cover letter from the school with my id details + the course details (how often, long the course etc), business licence, the director's id card, cooking class schedule. Only one of us as required to send further documents like pictures of the school, screen shot of the website.