Ray, I assume you’re talking about the pink or blue extruded polystyrene and not to flakey expanded white stuff?
I have done a little of experimenting with foam and bees :) I believe a prime coat + 2 coats of top coat will keep the bees from chewing the foam. However, there is a problem. Paint (latex paint in particular) has a tackiness to it that really doesn’t subside for months (maybe years?). This presents a real problem if you have something in contact with a painted piece of foam. The paint will generally prefer to stick to the other object rather than the foam. Hence if you used the paint as a barrier, it would eventually stick to the top bar wood body and pull away from the foam. Where it pulls away, the bees will most definitely chew!
I have been laminating 5mm low cost luan to my foam to keep the bees from it. However Windfall pointed out that luan is basically made from junk wood and hardboard might be more immune to winter humidity and mold growth. Hence I have switched over to using 1/8” hardboard laminated to foam to keep the bees at bay. In your application that might be a good solution too. It would give you something to pry on when removing the foam. ¾” foam all by itself is relatively flimsy.
I’ve tried gluing foil and polyethylene to foam using water based contact cement. It works OK, but it really isn’t a great bond. I suspect over time (maybe a year or two) the contact cement would delaminate in the humid environment.
I have tried foam adhesive as well. I think the stuff was called PL-300, comes in a caulking tube. It requires one surface to be porous and hence won’t work for many materials. Gorilla glue bonds well to foam, but not at all to some other materials like polyethylene.
You might try contact paper for a quick cheap barrier. Less work than gluing on hardboard. The ¾ pink foam sheets actually come with a thin (maybe a mil or two) polyethylene film over them. That seems unique to the ¾” stuff for some reason. It is not on the 2”, 1.5”, or 1” foam. Provided you don’t rip that polyethylene sheet off the foam, I would give you good odds that the bees would not chew through that.
Welcome to the wonderful world of foam and bees :-D