The outside of the hoof cannot hold bacteria, yeast, or fungus. The air and sunlight would kill all of the above. The best way to treat that would be to keep the horse in dry conditions outside and use a topical like Hoof Heal to keep the hoof from drying out too much. Hoof Heal has ingrediants in it that kill and prevent infection. Bleach would over-dry the hoof, making the peeling worse.
I think you may need a second opinion from a different farrier...
And you really need to post pictures when you ask for hoof related advice.
^^agreed. I've never heard of any bacteria/infection affecting only the outside/exterior hoof wall. Bacteria needs live soft tissues to feed on. Sounds to me like the farrier was feeding you a line of crap if this is what he told you. End result is the same, get a second opinion. Preferably a qualified veterinarian one, rather than a farrier that shrugs and says "put a little bleach on it, mmm-hmmm."