It depends on what type of anesthesia was used and if they got the dose right. If your bunny is older than 4, I'd want them to do blood work yearly to make sure he'll respond well to the anesthesia. Sometimes older livers and kidneys don't eliminate the drugs from the system as quickly as those of a young bunny, and animals used in lab studies of drugs (to determine the right dose) are usually 6mo-18mo old.
Injectible anesthesia might not be required for a routine trim. That would include things like ketamine, benzodiazepines, etc. Usually gas anesthesia is isofluorane or sevofluorane. They go to work faster and also go away faster. I think most vets use just gas anesthesia for molar trims, and injectibles for things like a neuter. However, when a bunny's mouth is open, it can be hard to get at the nose to get them to inhale the gas anesthesia, so it may be a matter of personal preference on the part of the vet to use injectible for molar trims. In the videos I've seen of tooth procedures, gas was used, perhaps in combination with a light sedative/anxiolytic like a small dose of ketamine or valium, and they pretty much had to have a second person there holding the gas cone on the bunny's nose, and that can be a lot of hands all in one tiny space.
However, you can make the argument that small animals like hamsters and mice are pretty much only put under anesthesia with gas, and they're even smaller to work with than a bunny's mouth and nose area. I had a hammie that had to be put under to be examined because she was very squirrelly and nippy, and although she was past the life expectancy for her species, she did just fine recovering.
I'd ask the vet if they wouldn't mind just using gas anesthesia, or only a light sedative instead of something that would knock him out for the rest of the day with the gas. Also, get some blood work done to make sure liver and kidneys are good. If their function is impaired, the drug might not be cleared as quickly as the dosing calculations assume, and that might make the effects last longer.
edit: Wanted to add that front tooth trims can usually be done without any anesthesia, but molar filing usually needs something. Also, drugs that make the animal not form memories of the procedure are often used with small animals like rats, combined with gas sedation.