Although the bugle does have an American look to it, I agree, I have never seen an American bugle badge with the cords. Here are a couple of pictures of those used during he ACW, and were still in use during the Indian Wars that followed. My ACW/Indian Wars bugle bugle has small, thin square shaped loops on the back (see first picture). The cap is a forage cap, but was worn the same on the kepi as well.
I agree, probably Belgian.
Terry