what you can do is: first take the veggie sprayer to the plant and hose it down both above and under leaves. this will cut back on the current population. Then stop at your local garden center or big box store....buy some ultrafine horticultural oil, or some Neem oil. Mix it, according to directions, in a hand spray bottle. add a drop of liquid dish detergent as a emulsifier. Shake well and spray your plant to make sure you are covering all the leaf surfaces. Place the plant in the shade until it is thoroughly dry. Do this 7-10 days apart for 3 or 4 treatments and that should solve your problem. Be sure to shake it well before using for subsequent treatments!
Spider mites don't seem to be a problem where the humidity is good. You may wish to look at keeping the humidity higher around your orchids. Also, if you saw these bugs in the medium, you may wish to repot the plant as well. Spider mites are very tiny and many times can not be detected on the leaf until the webbing gives them away or damage is seen.