Why is water turning white towels red?

I appear to have "red tide" in my water. We have city water that smells very chlorinated. If I go too long without scrubbing my shower, toilet, etc, there is red growth along with the usual mold. My towels (washcloths particularly) are turning red at the edges & the seams, where, I ume, they are soaking up the water & holding it longer than the rest of the towel. Hot water & bleach have not deterred this growth. I'm looking for a plumber or "water specialist" (is there such a thing?) that might be able to tell me what this red junk is & what counter-measures I can take. Thanks!