Controlling bird mites has less to do with specific insecticides than it does with eliminating the source of the problem (the birds) and then finding a way to get your product and the remaining mites together in the same place. Given how tiny these mites are this is the problem, in that they start crawling around the structure looking for a new blood host and end up within wall voids, in furniture, under beds and other furniture, under attic insulation, etc. So, your control program has to combine the exclusion of any birds, thorough and regular vacuuming of all surfaces to physically remove as many mites as possible (a good job for the homeowner to do each day), and applications of contact insecticides by you onto or into any likely places the mites hide or wander. 

Even dealing with the birds may be a legal challenge. Right now swallows are probably still nesting around a lot of structures, and as long as the birds are in their nests they cannot be molested, harmed, killed, or verbally insulted. They are protected animals, and you have to wait until they leave on their own, at which time the nests can be removed, the area treated, and a recommendation made to the customer that you be hired to install physical devices that prevent that nesting next year. If the birds are pigeons, sparrows, or starlings anything goes, as these birds have no legal federal or state protection. However, at least look into any local ordinances that may be in place that prohibit the killing or harming of ANY birds, which doubtless exists in some cities. 

Wherever the birds are nesting they need to be removed, any access into the structure blocked permanently, the nests removed and that area treated with a contact insecticide to kill any lingering mites. You might also dust the area with a desiccant dust as well to give long-lasting future kill of mites you miss initially. Be sure to wear the proper PPE while doing all of this, and if there is any accumulation of bird feces there is another opportunity for you to make money by recommending the removal of it and sanitizing of the area. Bird doo-doo is a great place for many human pathogens to grow, and these can be carried with dust and air currents into the breathing zone of people. 

Synthetic pyrethroids should be excellent products to kill mites, and they have liberal enough labeling for indoor uses to be used almost anywhere, including within walls with a deep void injector if you choose a product labeled for this kind of "fogging".