Pinto and 4-H are the only associations that have English Showmanship. I've only seen it done at Pinto World, as the club shows don't require it. 4-H shows are very different in Texas from other states, I've discovered.
Both organizations permit either an english bridle or a plain leather halter with lead shank. Since most showmanship horses are taught and cued with a shank, that's what most people use.