No, a dog’s mouth isn’t sterile. However, at least some of the bacteria in the canine system won’t infect humans so in that sense and from a human perspective a dog’s mouth is cleaner than a human’s. Every germ in a human mouth can infect another human, so if you have to be bitten, be bitten by another species, especially one with a different typical body temperature.
For example, very few reptile bacteria infect people (except for Salmonella) so a nonvenomous snake bite is preferable to a dog bite and much cleaner than a human bite.