There are several treatments for the ridding of bird mites, though most suggest/require removing cages from the home, thorough cleaning & treatment outside, before bringing back into the house. While there are numerous sprays available online, from veterinarians & pet stores, the only thing I have ever used was Sevin dust, rubbing the powder into my bird's feathers and not letting them bathe for several days.....
I did 3 treatments of 3 day durations, where I removed everything from the cages, vacuumed the cages, being especially diligent of corners & under edges, washed toys & perches in hot soapy water & let everything hang in the sun to dry. Three days later I did it all over again and again three days after that.....before putting toys & perches back in the cages, I dusted the cage floors with Sevin Dust, laid fresh newspapers under the floor grate & re-dusted on top of the papers.....
Unlike fleas, mites crawl to their next meal, but when I cleaned & treated the birds & cages, I vacuumed the room's carpeting & re-dusted with Sevin Dust.....when dusting your birds, they should be completely dry.....
Ten days later I couldn't find any sign of mites.....
You can contract with a pest control company, but you still have to clean your own bird cages, perches & toys, so, while doing that, why not just spend the extra $12-$15 for Sevin Dust, instead of a $65-$150 pest control treatment.....
Here's some information on bird mites from the University of Minnesota & a couple of government agencies in Australia:
BIRD AND RODENT MITES IN HOMES
http://www.health.sa.gov.au/pehs/PDF-files/ph-factsheet-bird-mites.pdf
Bird Mites
In answer to your question, I'm not really sure I would wait for my visit, because, unlike fleas, which are active all the time, mites are normally nocturnal pests and don't venture far from the feeding station (bird's blood source) and since the weather pretty much guarantees you're not going to be wearing one of your furs, I doubt any mites would look to you for a taxi ride to visit your birds.....now, I probably wouldn't get in the cage with your friend's birds...arms/wings length is probably OK, while visiting, but aside from just being a pain in the butt, you're not dealing with cholera or typhoid.....
Good luck.....