Do you have a reason to suspect an unusual source of mold (e.g., water leak, poor ventilations, etc.)? If so, you need to fix that problem or you will never stay ahead of it.
Otherwise, minimize the humidity in the room and just assume there is mold and disinfect.
Mold is pretty much everywhere as airborne spores unless you're in a special "clean room". But you can avoid mold blooms by keeping the humidity in the room below 50%.
- Run an exhaust fan during baths/showers, and for long enough afterwards to get rid of the humidity.
- Leave the bathroom door closed while the fan is running so that you exhaust the humid air in the room rather than just sucking conditioned house air directly from the doorway into the fan.
- Wipe down the shower or tub after use with a towel to get rid of water clinging to surfaces.
- Leave the bathroom door open when not in use so the room air stays well mixed with conditioned house air.
Most of the disinfectants use either chlorine or benzalkonium chloride (a generic term for a collection of chemicals with names like alkylbenzyldimethylammonium chloride, often with several different related compounds in the disinfecting solution). The latter type is what is commonly used as a general purpose disinfectant in healthcare settings and is in some household disinfecting cleaners.
Both types work. Disinfectants need time to work so the most effective way to use them is to clean first, then spray them on and let them dry rather than wiping it off. Chlorine type disinfectants may show faster visible results, but they work only until it dries. The benzalkonium chloride disinfectants can continue to act as a mold retardant if you leave it in place (it also smells better).
You can also clean surfaces with certain common household chemicals, like borax solution, and leave a film of it rather than rinsing it clean. It will retard mold growth.
Do a thorough cleaning and disinfecting at least once per week. If you see mold growth anywhere, clean and disinfect that, then do the routine prophylactic treatment more often.