[Wavery]

The issue that you are experiencing with this type of mold is not growth of mold on the surface of the caulk. If it was, bleach would absolutely kill it and make it disappear like magic.

The problem is that the caulking was applied on a humid day and the mold spores embedded themselves in or under the caulking. Once the caulking has cured, the mold is allowed to grow inside a protected shell. No amount of chemical of any kind will penetrate through to the mold. If it does, the caulking would also be removed.

I would live with it until a very dry hot period. Remove all the old caulking and wipe the surface with acetone (acetone will disperse moisture) to remove any residual moisture (be very careful to get out any moisture under the moldings). Then lay down a new bead of caulk.

We don't have this problem on our campers in SoCal but we do in the calking in the bathrooms, if the moisture is not properly removed before installing the caulking. I manage a 40-unit apartment building and have 80 bathrooms that I deal with. I used to hire others to do all the maintenance. After years of problems, I do it all myself now. It took me several years of struggling with this issue of mold in the caulking before I figured out the real issue. Dap, makes a caulk that is advertised as "Mold resistant", I tried it with the same results. For the last 6 or 7 years, I have wiped down the joint with Acetone and the mold has never reappeared in those bathrooms.