I have black "tar/mold" looking stuff coming up from my bathroom sinks. Its so gross. I have tried cleaning it with bleach and it always comes back. Now one of the sinks won't drain. I found two little black worms that move like caterpillars. There no more than 1/4 inch long. They can float in the water. Once they get to a solid surface (like the bottom of the clogged sink they will start crawling on the sink, underwater. What are these things? Is it caused by that black tar/mold stuff coming up through the sinks?

Your drains are clogged. Call drain cleaning company to snake your bathroom drain. This problem won't go away until you deal with it. Hopefully, the caterpillars will vanish with clean drains...