The thing is, you're using 'suspenders' perfectly innocently, but over here those'd be called 'braces'. Suspenders are the things one uses to hold up sexy stockings!
Oh, and you could try attaching something to the bridle with a loop he can put over his head and hang around his neck - but don't just use string or it'd cut into his neck. Have you got a handy piece of flat tape or a strip of fabric? Though if the head is heavy it probably wouldn't be good for his neck and attaching it to the braces might be best.