SA, I take it?
Hate to say, but 1/3 the world away, I don't have an informed recommendation. Google popped up with about 4 listings in Cape town who specifically have an avian vet on staff, but I can't say if they are any good, nor how much they will charge, just that they claim to be qualified.
Here in the US, the visit fee itself can vary wildly from vet-to-vet and wouldn't correlate to your costs anyways. That being said, most vet offices would be happy to quote you the expected base checkup cost with the understanding that any tests and treatments would be extra. Simple tests and treatments are generally inexpensive, more complex ones not so much. If it is indeed mites, a quick sample and glance in a microscope will confirm they are present -- pretty simple. If it's not, it will depend on what the vet finds at each step, but that's a good thing -- the vet is dealing with the real problem, not the one you thought you had.
As for supplies, I know Ivermectin can be purchased online in various formats, and is fairly shelf-stable, but I'd be shocked if any vet office pretty much anywhere in the world didn't have some among their on-hand supply. It is so ubiquitous, functional and cheap that there are claims it has even driven a few used-to-be-common parasite species to extinction. Even if they don't have it, they'll know the local places you can pick it up.
To give you context . . . When our conure (and a friend's budgie we were bird-sitting) had to go in for mites, the visit was short and relatively inexpensive -- base cost for the visit, nothing for the test (covered in the checkup) and a nominal fee for the one dose of Ivermectin for each bird, which was topically applied. We also picked up a pyrethrin cage spray specifically diluted for birds that they recommended to drive off the mites. The behavior changed within the hour and the problems fully went away in a few days. Again, near miraculous, but if I'd skipped the vet, wandered down to the local farm supply store and bought the horse-and-cattle version, the story probably would not have ended well.