I use deer rawhide also. Nice and thin. I like to glue the flesh side because the hair side is easier to decorate or paint, if you will. Crisper lines with less bleeding. Also, its the way I learned.
I figure that the ace bandages breath, so that's why I leave them on a bit. However, I have taken them off after an hour or so with good results. I guess it mostly depends on when I rawhided the bow. Likely, because it was midnight when I started the process and I got to get to bed.