I agree. Bathe away. Remember, dogs (and humans) don't "get colds" from getting wet and cold. They get them from viruses. Being cold for too long can make your immune system weaker, making you more susceptible to colds, but even if you get wet and cold for a while and lower your immune system, you can't get a cold unless you come into contact with a cold virus.
BTW, dogs and humans cannot share cold/flu viruses. :)