I just despise seeing the mildew and mold that creeps into the bathroom or in a dark, damp basement. Both of them are part of the mold family of fungi, with mold often being black, green, red, or blue in color while mildew is usually gray or white. No matter the color, I hate to see it creep around the caulking of the bathtub.
flickr/cc - iLoveButter
The ways I have found the have helped, whether in a small or larger way, are preventive measures and regular cleaning. When used in combination they seem to keep the bathroom clean until time takes it's toll on the caulking and it needs to be replaced.Preventative:
➠ Keep toiletries and soaps to a minimum on the counters and inside the tub as water collects around these objects and allows the mold to grow.
➠ Consider hanging a shelf outside the shower with your toiletries, as this will allow your products to air-dry completely, avoiding mold growth.
➠ When cleaning the bathroom, remove all items from the surface and before you place them back, make sure they are thoroughly cleaned and dried.
➠ Keep the window in the bathroom cracked or a vent on while taking a shower and leave on for a few minutes after to help suck out the moisture. If you have neither, keep the door open, if possible, and open a window in a nearby room.
➠ Use a squeegee or towel to dry the shower walls and along the caulking
Cleaning:
Always be sure to wear gloves and face mask, keeping vents and windows open to cut down on fumes and the toxic affect mold and mildew have.
➠ Plain old soap and water can be tried first if the growth is not too deep or too severe.
➠ Use bleach chlorine, however it is best to mix with water as overtime it can break down the underlying surface
➠ The other alternative is a paste of baking soda and white vinegar smeared onto the surface and left to dry, then scrubbing off and repeating as necessary.
➠ Hydrogen peroxide can be used if mixed 1:2 with water and sprayed onto the moldy area and scrub to remove.
➠ Other options: Grapefruit seed extract (20 drops to 2c. water), Tea tree oil (1tspn to 2c. water) - The smell of the tree tea oil can be strong but after a few days the smell will dissipate.
Repair:
➠ The caulking may just need to be removed, cleaned and replaced. Don't do like the above picture and just place new caulking over the old. This will make matters worse down the road.
➠ Also consider that mold may have grown inside faucets, shower taps, etc and you may have to replace those to fight the mold.
flickr/cc - xJasonRogersx
Really, mold and mildew aren't to be feared, it is just a matter of staying on top of it and when preventative measures and cleaning don't do the job, it is time to take it apart and start over.
Murphy's Oil soap also works to clean mold. Your big box hardware also sells some natural liquids (usually in roofing or siding isle) that do a great job. As you pointed out you have to avoid corroding the surface you wish to clean which makes bleach tricky. With bleach once you kill the area rinse and clean it.
Consider leaving your shower door or curtain open an inch or two on both ends to promote air circulation of course this is when you aren't showering.
Boiling Water helps a lot. Get an old teakettle, fill it with water & put it on to boil. When it's nice & hot, pour it over the mold (Be CAREFUL while you do this - It can burn you). This kills the mold in place & then a little light cleaning (for example, wiping it down with a rag & some cleanser) will do what would otherwise have taken a lot of hard scrubbing.
It also takes a lot longer for the mold to come back after such a boiling, since most of the mold died when it got boiled.