Here is an excerpt from the site of Margaret A. Wissman, D.V.M., D.A.B.V.P., a very highly respected vet in the US. This article is from a forum for other vets, so she's teaching other vets how to work with clients whose budgies have mites:
"The most commonly encountered mite is the scaly face mange mite of budgerigars, called Knemidokoptes pilae. It is found on the cere (that fleshy portion of skin over the beak where the nostrils are situated), the skin around the beak, around the vent and also on the legs. This mite burrows in the skin, causing a powdery appearance to the skin, and if you look closely, you will see a honey-comb pattern of holes in the skin, representing burrows and tunnels caused by the mites. These lesions are usually not itchy... Diagnosis is usually confirmed by skin scrapings performed in a veterinary office, and then examined under a microscope. Older remedies included applying mineral oil or ointment to the lesions, to suffocate the mites living under the skin. Treatment of choice is the administration of ivermectin, either by injection, orally or topically. This should be administered by an avian veterinarian, based on the precise weight (in grams) of an infested bird, dosed carefully after calculation of the exact amount of medication necessary. Treatment should be repeated at 7-10 day intervals for at least 3-4 treatment. If the mites have deformed the beak, it may need to be trimmed by a vet, as well. Although these mites are not thought to be easily contagious, it is best to treat all birds in the cage with an infested bird. The mites cannot live off of the bird and they cannot cause problems in humans or other species of animals.
There is one mite that you cannot easily see. The air sac mite ... One other type of mite may be seen in pet and aviary birds. This is called the red mite (Dermanyssus). This nasty mite bites birds and sucks their blood...
Several products are available for you to sell to customers with mite or lice problems. The safest and most effective products should contain a percentage of insecticide (pyrethrins or carbaryl) that is safe for birds, yet will kill the parasites. Sprays or dusts are safest.
Ointments generally should not be used on birds, because if spread over feathers, they will prevent proper thermoregulation of the body temperature by the bird. Any products for use on birds should not contain lidocaine (a topical anesthetic that is toxic to birds even in very low doses). Products safe to kill parasites in cages and cage equipment can be offered to assist the owner with their problem. If you see mites or lice on a pet bird brought in to your store, you will never go wrong by recommending that the customer take the bird to an avian vet for diagnosis of the specific type of bug present, since it is now obvious to you that different insect parasites require different treatments."
The bolding is mine, and the ellipses (...) mark places where I left out info I think is irrelevant to your situation. To read the full article, go to
www.exoticpetvet.net and look in the Table of Contents (lower left margin) for the article titled "Of Mites and Men."