White vinegar works really well, as it kills the mold spores whereas bleach does not.
I've had this problem. I cut out old moldy caulking and sprayed mold spray, then javex not together tho. Fill tub up and put new caulking on. Once dried empty tub. It will put a good seal on it. Weight of water opens up the seam allowing more caulk to adhere. Good luck.
The first step is to figure out why you have the mold stain. Is it coming from wet caulk or is it coming from behind the tile? You can kill the surface mold with vinegar, but if it's coming from somewhere else, it will continue to come back until that part is fixed. If it's just in the mold, it is a good idea to scrape or cut the existing mold out and replace it with waterproof caulk. Doing that will allow you to figure out how deep the mold is growing and your new caulk should really prevent more mold from returning. I hope this helps you. Wishing you the best.
Have you seen this? https://www.hometalk.com/2575788/discover-a-new-way-to-stop-mold-mildew