Ordinary household bleach will clean out your camel back just fine. It kills microbes fairly effectively. I would think you probably have some form of algae in there rather than bacteria, assuming you use water in the camelback.

Just be sure to dilute the bleach before throwing it in and a small amount of bleach in a quart or 2 of water does it (like was said before a "capful" whatever that is). The notion of running through some mouthwash to get rid of the bleach taste sounds good.