Dehumidifier
Looks that despite your efforts, there is enough moisture long enough, for mould to grow.
Other little things that might help are:
To remove wet towels from bathroom and also use towel or some other absorbent rug to soak up the remaining water from walls and floor after shower, so time from shower to dry bathroom is even shorter.
I think that some kind of mould killer has to be used, to reduce number of spores.
Unfortunately mould that grew into grout and under silicone most probably has to be scraped out, and tiles re-grouted with mould resistant grout.
Another big gun would be dehumidifier, or portable airconditioner on top of wiping dry the shower, as on wet rainy day opening window does not remove enough moisture to stop mould growth.
I know that Harvey Norman can get one for you,
or you can try them direct:
http://www.delonghi.com.au/