Kate,
First let me say I don't have any experience with cows or treating cows for flies. I don't know what Permeation is, is it a process or a chemical? I tried to look it up on line, but could only find a process. So if that is the case, you first need to know what chemical or product you are using. Whatever it is, you should be able to contact the manufacturer for recommended application protocol, and whether it is toxic to bees. (That may be on the package of the stuff you are considering using.) Once you have that information, it will be easier to decide a course of action. I welcome input from others as well.
Dennis