FYI: The use of natural oils and other substances in the pursuit of mite control in honey bee colonies. This document mainly covers the calibration of LD 50 doses of essential oils with respect to honey bees.
David A. Cushman's web sitehttp://www.dave-cushman.net/bee/naturaloils.html
Control cages that were fed sugar syrup had an average of 2 dead bees over 72 hours. Bees fed the ethyl alcohol sandwich without any oils had an average of 3.5 dead bees over 72 hours. Thus, the physical effects of force feeding were minimal and the ethyl alcohol we used had little toxicity for the bees.
The following is a list of the approximate LD 50's for each of the oils tested together with menthol from a previous experiment.
Substance LD 50
Menthol unable to cause mortality with highest doses administrable 
Cinnamon oil 150 ppm
Clove oil 200 ppm Pinene 1500 ppm
Thymol 100 ppm
Oil of wintergreen 500 ppm.
Neem oil from 100 ppm to 1000 ppm (the bees did not take well to being fed Neem oil)
Establishing the toxicity of these potentially useful botanicals is an important step to understanding dosage response, and the risks of administering these materials orally to bees for their protection against mites. Although a given compound may be efficacious against mites, if its toxicity to bees is high then there is great risk in using it.
Materials such as thymol may continue to be useful as fumigants and in topical application, but would have to be used with care as an oral medicament. Pinene, on the other hand, may be valuable in killing mites on and in the bodies of honeybees by its relatively low toxicity to bees when they ingest it.
If you do a web search on Pinene you are in for a surprise!