Mildew and Mold in bathroom....... HELP HELP

The last house we owned got some serious mold/mildew in the bathroom. Crazy pink stuff all over the shower walls (plastic walls), near the faucets and totally all over the caulking. Sometimes it would be brown. Even if I would scrub (which yeah, I should have done more often), it came back within a few days.

This didn't seem to be much of a problem at our new place. We've been here a few months, and now I'm noticing it growing on the caulking, near the shower door, under the faucet, and on the tiles. This shower is different than the old one. The other one was a solid plastic wall, while this is tile and a sliding door.

I had been cleaning every two week and spraying with clean shower, but didn't do either for the last month. Neither bathroom had an exhaust system. I scrubbed and srcubbed the new mildew here and it doesn't seem to help, ecspecially on the caulk.

I really, really, really don't want a yucky mold covered bathroom again. How can I fix and prevent this? Is there a way to re-caulk over the old caulk? Because it doesn't seem to come off of the caulk. Yuckkkkkk. Any links on mildew cleaning, or caulking?

Thanks