Remove black residue/mold on bathroom caulking
I am afraid there is no simple solution for this. 

One of the issues you might have is that these locations are damp by nature ; and they might be poorly lit. Damp/Dark = Mold growth. 

Now in the modern world of LED lighting people will say it is not poorly lit so it is not dark.
 Point well taken EXCEPT that LED light lacks the UV rays needed to inhibit and kill mold growth. This is why I have Halogen Lights above my shower and not LED lights. So now instead of having a terrible mold growth and cleaning problem every day, I have an easy to keep clean area with no visible mold growth anywhere.