Personally, I don't use bleach either...not when there are man other options that are equally as effective yet not nearly as toxic. Two options you'll commonly see recommended on this forum are chlorhexidine gluconate and QUAT based disinfectants.
Chlorhexidine dilutes down to 2 ounces to a gallon of water (yes, 2 ounces to a gallon!), and is pretty effective at removing common pet specific microorganisms. Whats nice about chlorhexidine is it doesn't need to be rinsed, has virtually no smell, and can even be sprayed on skin (its commonly used as a wound wash. Avoid contact with mucous membranes). Simply spray on, let soak for 20 minutes, and wipe dry...no need to rinse. It leaves the surface aseptic for a day, preventing any new bacteria from taking hold. You can find the concentrate online for about $20. This is enough to make 64 gallons of disinfectant.
http://www.reptilesupply.com/product.php?products_id=3061
Another option is a quaternary ammonium disinfectant. These come under a variety of brand names, but are non-toxic once diluted and don't need to be rinsed. They are commonly sold as either a disinfectant/cleaner combo with detergents, or a pure disinfectant. The pure disinfectant varieties have no color or smell, and don't need to be rinse. The detergent varieties usually don't need to be rinsed either, but commonly come with strong fragrances and need to air out before you place the dragon back in the enclosure. Either variety is extremely effective at killing all kinds of microorganisms...much more so then chlorhexidine, and even more effective then a bleach solution.
Prices range...and the true "hospital" grade varieties get expensive. However you can get Simple Green-d Pro 3 from home depot for $15 a gallon. It dilutes down to 2 ounces to a gallon for strong cleaning, or 1 ounce to a gallon for quick cleanups. I use it at 1 ounce to gallon, and it has a very faint herbal smell...airs out in about 15 minutes and doesn't need to be rinsed. Very effective deodorizer for a messy dragon. The Pro 3 contains detergents, however hey also make the Pro 5 variety which is colorless and orderless...simply a disinfectant, and it too is around $15. Sold online or at office depot IIRC.
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Though it may not seem like they need it, I routine disinfection is a good way to keep you and your pet safe.