I did a little looking online and it appears that a rabbit and a cat can both get a variety of mites. It said that the rabbit or the cat may not show any signs, but that in a cat – since they groom so often – you can sometimes tell if they have mites from their feces, so you may want to ask your vet before your visit if you could bring in a sample of the cat’s feces and if he or she could tell from that sample if your cat has mites. I would imagine a cat and a rabbit would get similar treatments – but you’d have to ask a vet or someone who is more familiar with cats.
$46 for a vet sounds reasonable, and did you ask if they take a credit card? That might make things easier for you. The things about mites is they can spread on the rabbit and the rabbit can lose quite a lot of hair, and it can cause other problems, so its probably more inexpensive to treat the rabbit right away. I don’t believe the vet should have to run any tests for the mites, but you will probably have some fee to pay for the mite treatment.
Good luck – let us know what the vet says!