I would ask about other treatments as well...I'm not a fan of putting something so harsh as bleach on my animals, there's got to be something better than that, imho. Did the vet even tell you to dilute it? Surely he wouldn't recommend you to put it on full strength? I hope not, because you may just wind up burning your poor horse's skin and coat, quite literally. I know you want to get rid of the fungus, but there ARE better ways than using such a harsh chemical on him. Yes, use it in the barn, and on everything you can, but I would be very leery of using it on the horse itself.
Try to get some kind of fungal shampoo...I know vetrolin has alot of really good shampoos. There are also others, but they are totally blowing my mind right now...go figure. Chlorehexadine will disinfect the horse, prior to bathing, just as well as bleach, and you should be able to get it at any decent fleet supply, or good tack shop.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."