I can't believe people actually use bits like those! We normally ride in a simple d-ring or loose ring snaffles or rope halters with our horses, and I don't think we would need much more for a mule.. The only problem I could see would be getting a bridle/halter over their ears and keeping the saddle from sliding, but breeching(sp?) could help with that.
The mule will definitely be already trained, I haven't fully started a horse yet(though I have helped a few people do so) so I don't think trying with a mule would work out for either the mule or myself.
I am in the process of finding a trainer and I will pick the owners brain, I normally do when buying any animal. I'm not going to be doing this on my own, but I am sure it will be a learning experience...
That's what won me over, when I was about 9 we saw a mule at a show, and WOW was he amazing! Trust me, there will be tons of pictures! It isn't set on which one we are getting, but I will be sure to post pictureS when he/she arrives!