How do I remove mildew from my bathroom?

Have you tried tea tree oil? Look at how this hometalker used it: https://www.hometalk.com/diy/clean/bathroom/the-best-way-to-remove-mold-mildew-with-2-ingredients-no-bleach-33077514

Depending on where the mildew is, I use bleach soaked cotton coil to remove any stubborn stains in the bathtub. I let it soak a couple hours to bleach grout/caulk if needed. Vinegar kills mold and mildew, but sometimes the stains can be so stubborn and bleach helps!

Proper ventilation - fan or open window should be running/open during showers or baths to prevent mildew or mold. There are good mold killers available. I would probably re-paint afterwards using Kilz or Zinzer primer and then a good latex enamel top coat to cover the old spots.

After removal keep bathrm dry open doors(shower,actual bathrm), use vents exhausts,wipe down any remaining water on shower walls,ceiling, or anywhere else in room after using it. Hang towels out well so they dry & don't retain additional moisture.