How do I wash the fur and eliminate any possible bacteria while keeping it looking natural?

Use a typical pet-shampoo with a flea and tick killing chemical. Bacteria would more likely be the result of what's on the inside than the exterior fur. As long as you treat the hide properly to dry the tissue before bacteria takes hold, you won't do any damage to the fur. If the bacteria starts to degrade the skin, you'll lose the hair no matter how you clean it. In fact, letting the bacteria go for a few days is one way to de-hair a hide. Hartz or a similar brand of pet shampoo will not only clean the fur, it will help to remove any remaining fleas, ticks, or more importantly, mites, which eat the fur and skin.