Baby aspirin is considered a safe med for rabbits, but it can sometimes cause gastric irritation and like any medication, needs to be used appropriately and with caution. It also should NEVER be used if there is bleeding(internal or external) or following surgery. Aspirin is a blood thinner and if there is any internal bleeding, the aspirin could worsen this bleeding and further complicate the situation. For this major reason, I didn't think it wise to mention it's possible use as it is contraindicated in this type of situation. Pain control is important, but it is also important not to use something when it might cause more harm than good. Metacam is a much safer NSAID to use with rabbits, and won't thin the blood like aspirin will.
Another thing to keep in mind is that pain isn't as likely to be the cause of the lack of appetite immediately following the surgery, as a rabbit will still have pain medication in their system from the surgery. Usually the biggest cause of nausea and lack of appetite in the first 12-24 hours(and sometimes even longer) following surgery, is the after effects of the anesthesia. One way to know if the anesthesia is more the cause of the lack of appetite than pain, is if the rabbit is starting to hop around and move more, but still doesn't want to eat. One of my rabbits took 48 hours to really get back to eating normally, primarily from the anesthesia making him feel sick. He was hopping around fine, just wouldn't hardly eat. So even if you had pain medication to give, it still may not have made a difference in helping your rabbit want to eat, if the anesthesia is the cause of the lack of appetite. And with that it just takes time for it to wear off.
With my rabbits if there was just one thing they would eat, then I would just keep offering it to them. Since your bun is eating parsley, that is something to work with and keep encouraging. She should start wanting to eat more as the day progresses.
There's really no way of knowing beforehand if a vet is going to be good, even with a recommendation from another rabbit owner. Their recommendation will be based on their experience, and they may not know themselves that the vet isn't a good rabbit vet if they aren't very experienced with the correct and normal treatments for rabbits. Only way to know is to become more knowledgeable yourself, so that you know the right questions to ask, and even some of the appropriate treatments for the more common ailments in rabbits.
Spay surgeries are quite stressful to deal with. I don't think many vets warn owners about the difficulties that can be encountered afterwards, and it is something they really should do.