I tried so many hings. I was close to ripping all the caulking out completely and replacing it. I didn't want to but I was at the end of my rope. As my last effort I tried this method and thank god it worked. It worked so well.
A quick note. I would recommend eye protection and large gloves to protect your hands. Don't wear something that a few drops of bleach might ruin. My dress got hit with a few drops but its tie-dye so that's okay. Please have the fan on the whole time and no kids or pets around. Bleach is dangerous, be careful. It may also ruin the caulking. It did not ruin mine but the risk still exists that yours may be ruined. This is really a last stitch effort before you remove the whole thing.
With that out of the way, here is how to make mold disappear from caulking:
Plug the sink or use a basin.
Ripe off many pieces of paper towel. The half size paper towel is best for this. Place them in the sink.
Pour bleach over the paper towels to saturate them.
Remove a saturated paper towel and squeeze out some of the bleach so you don't drip it everywhere like I did. Squish it right against the caulk like pictured above.
Repeat many times until all the moldy caulking is covered.
Leave the fan on, close the door and leave it for a few hours.
After a few hours, check under one of the paper towels. If there is still mold, leave the paper towels in place a bit longer. If the mold is gone, discard the towels and rinse everything.
Enjoy your mold free bathroom :)