It varies so much. My 6 year old chronic snuffly bunny was in for a dental on Tuesday, she was done around 2pm and was up bouncing about and eating normally by 4pm! But I know of other younger, perfectly healthy bunnies who can take a good couple of days before they are themselves again.
It also depends on what anaesthetic protocol is used as there are a few different options that can be used depending on the rabbit. Some people find that their older/poorly bunnies wake up more quickly if they have had a gas only GA but I seem to be fortunate that my little one is fine with the injected induction (there is also a reversal agent that can be used with this). Most vets prefer to use the injectable anaesthetics to start off with as the gas only stings and smells odd so it isn't very pleasant for the rabbit.
My vet also routinely gives sub-cut fluids (as well as painkiller etc) and this does seem to help them to recover more quickly, as the fluids keep them well hydrated and help to flush the anaesthetic out of their system more quickly.
So, not terribly helpfully perhaps, the answer is "it depends". It can be anything from - fine pretty much straight away, through to a good few days. The key thing is that if there isn't much improvement overnight, to go back and make sure the bun is given adequate meds such as pain relief, gut stimulant etc as necessary to help them to recover.