not 100% sure but 95% sure not honeybee and know not bumblebee. maybe paper wasp or yellow jackets? They are mainly around my hummingbird feeders and around my back door. just don't want them building anything in the coop and having me go in there and getting stung. I am not "allergic" but last year I was stung near my elbow and my arm from just above my elbow down swelled up about 2x the size and was itchy for about 2-3 weeks! My main thing is just keeping them out of the coop. And yes it is normal window screen.
It might be good to make a new thread about keeping wasps and bees out of the coop. That way people who have good ideas will know you need help and people who need help can easily find the thread because of the title.