I have always used distilled vinegar for removing and killing mold. Chlorine bleach is good for non porous surfaces but it is a harsh chemical and can damage the surfaces and it gives off harsh fumes. Bleach cannot completely kill mold growing in porous materials. The chlorine in bleach cannot penetrate into porous surfaces such as drywall, wood and grout. The chlorine is left on the surface of porous materials and only the water component of the bleach is absorbed into the material, providing more moisture for the mold to feed on.
Vinegar is a mild acid which can kill 82% of mold species. However it also has the advantages of being natural and safe. Vinegar is non-toxic and doesn't give off dangerous fumes like bleach does.
To kill mold with vinegar, use white distilled vinegar which you can buy cheaply from the supermarket. Pour some vinegar into a spray bottle without watering it down. Spray the vinegar onto the moldy surface and leave it to sit for an hour.
Wipe clean the area with water and allow the surface to dry. Any smell from the vinegar should clear within a few hours. Good luck.