If the tiles are only mildly affected you could dry a solution of Milton or other similar brands of baby equipment steriliser.

If there is extensive black spot mould then I would recommend a proprietary anti-fungicidal tile cleaner from your local DIY merchants/ Screwfix or even Lakeland.

Once clean, it would be worth investing in a hand held vacuum tile cleaner as this will ensure that the moisture is removed from the tiles following a shower and not allowed to remain in the tile joints and allow bacteria to form.