In 2003, some folks (one who happens to be someone I went to high school with) brought out the Freshmakkur, a rather complicated way of purifying their grey water. Their website is :
http://www.freshmakkur.org/tech.html . Their whole system is too elaborate for most camps b/c most people don't intend to reingest their water. HOWEVER, their tips on deflocculating are invaluable: I used alum last year to precipitate out much of the nastiness from our kitchen grey water before putting it in our evap pond. Filtering the shower water is tougher in that it is usually generated in much higher volumes so therefore harder to manage. Fortunately, it's generally lower in the VOC's than kitchen dish water, so it tends to stink less. You can still do it, you just have to find a way to capture the shower water (a sump pump would work well for this: I have one that runs on D Batteries, and I know they also come in 12 volt models that can be run off a car battery).
If you want to hurry up the process after putting bleach in the water and waiting the prescribed amount of time, you can pour your water slowly through GAC (granular activated carbon) You most commonly see this in those Brita filters, but it's only a tiny amount (hence the reason they don't LAST very long). GAC removes the bleach and also many VOC's from the water. The easiest way to do it would be to purchase loose GAC from someone (you could try Orchard or Home Desperate, or my choice since I worked there, U.S Pure Water Corp. in Novato, CA) and fill the bottom half of a bucket with it. You could put a hole in the bottom with a fitting and a ball valve so that you can empty from the bottom. you would also need a fine mesh (think window screen) lining the bottom. Even this may be too much for most camps so of course you can just wait for the chlorine to decompose in the sunlight. I've been working on ideas for this for 2 years now, am still struggling with balancing the work load vs. running around having fun dilemma. The more processing you do to the water, the less time you have for "fun", but it makes me feel better about strict adherence to LNT...