Yes, Bifen IT is safe to use on St Augustine. Be sure you are not spraying during the heat of the day as the water can magnify the sun rays and scorch your grass.
Bifen IT is not labeled for Bermuda mites (eriophyid mite) but we would advise to consider a product like Triple Crown T&O Insecticide.
Triple Crown T & O Insecticide is specifically labeled for the Eriophyid Mite and applied at 7.5 fl oz per 100 gallons of water (0.07 fl oz per gallon of water). Per the MITES footnote on page 5 of the product label, to ensure optimal control of eriophyid mites, apply in combination with the labeled application rate of a surfactant. A second application, five to seven days after the first, may be necessary to achieve acceptable control
We do sell professional Roach Bait Gel and Ant Bait Gel. Follow the links to which ever one you are inquiring about. We also carry bait granules and insecticide granules for pest control. Please read the labels for specific instructions on application.