Once I saw the surgeon, they submitted the paperwork and I got an approval letter in a couple of days. I think, though, how long it takes depends on the insurer and their criteria, Good luck!!!
I have Cigna. I did all my requirements (6-mo diet, etc.) & my paperwork was submitted ~ Dec 18th. I received an approval letter on Jan 16th, so almost a month wait, but it was around the holidays too. They told me that they have 45 days to review the request.