Black Ring in bathroom sinks and bathtubs

I really don't know if this is the appropriate place to ask this, but I thought I'd give it a shot. My husband and I just moved to a house. We noticed that all of the bathroom drains have this black ring around it that just won't come out. I poured bleach down all of the drains and tried scrubbing it, but it only eliminates some of it -- the rest of it seems permanently stained and it looks horrible. I really have no clue what is causing this black color and what I can do to get rid of it. I can take a picture if need be. We have very hard water in this area.

Yes...post a pic

Here are two pictures of the black rings. They were a lot worse, but I've been scrubbing them for days. It seems that bleach aggravates them. When we spray Tilex to clean the tub, it definitely exacerbates it. The rings were present when we moved into the house. It takes a lot of scrubbing to get it to go away. In one of the sinks, it looked slightly purple when I was cleaning it.

Those drains come with a black rubber gasket that is often placed under the drain flange and break down after time...You could try and remove the drain and see if that is what is causing the problem...It looks like it from the pic...if it is use plumbers putty in place of it...

Thanks for the fast reply. Just to clarify, I should replace the rubber gaskets with plummer putty? I am concerned that with all the bleach I used, I've greatly worn them out. Could this lead to a potentially bad leak? How hard is it to replace the rubber gaskets in the bathtubs and the sinks?

Are the tubs cast iron?

I'm really not sure how to tell if they are or not. I do know that the house was built in 2003, so I'm not sure if that will help or not. The tub itself is one piece with the shower, if that makes sense -- there is fake grout. We are dealing with a leak in one of the tubs. Four days after moving into the house, we noticed that the ceiling above where the pipes for the tub are were wet. We filled the tub back up to see if the leak would occur again (my father in law came to assist since he is good with plumbing) and it didn't. I'm not sure if the wearing out of the rings may have something to do with it.