OK, that seems right. I have never seen won like that, but it is a smaller version than the one I have. I also feel the insert is very probably separate from the bugle. The mounting pins also seem right. I also believe it is just an infantry bugle as that was the symbol for Union infantry at the time. Musicians would have worn the same, but with lace on their dress tuni.If vintage would be worth a good $75-$100 USD, if not more.
More here
https://www.google.com/search?q=unio...w=1920&bih=937
https://civilwarwiki.net/wiki/Union_..._the_Civil_War
https://www.tapsbugler.com/civil-war...-the-bugler/4/
Terry