My son had to have dental work done under IV anesthesia when was 2 and the pediatric dental office had an anesthesiologist come in. It was totally fine and my son did really well. I was able to speak with the anesthesiologist way before the appointment so I knew that the drugs he used were safe in a non-hospital environment. There are many many IV anesthesia drugs, some are safer than others and easier to "reverse". (Just as a side note, I hated to have to put him under but I understood why they wanted to. Also, we got the news from one pediatric dentist and after talking with the anesthesiologist she used I just about came unglued. It was totally not okay with me the way they handled things so I shopped around and found the dentist we use now, with the better anesthesiologist. So don't hesitate to get a second opinion I say. Any doc/dentist who gets offended doesn't need to be your doc/dentist. I am sorry about the cost though. My dental insurance didn't cover much of the anesthesia cost either, but if we had gone the hospital route then our wait went from 2 to 6 months to 1 year at least. I doubt your situation would require a wait that long for the hospital but my son needed to have surgery not wait a year or more, so we just paid the anesthesiologist.
Good Luck!
S.