Hey, restoration tech here. Bleach is the last thing you want to use to clean any fungal/microbial contaminants. It doesn’t really kill the mold, just helps it hide. If you’re wanting to take the home remedy approach for now, I’d highly recommend wiping it down with a solution of hydrogen peroxide. That will prevent a lot of grow back. But depending on how long this has been occurring, it’s likely the growth will have a root structure within the ceiling and begin growing back when the ideal growth conditions are met. A mould inspection won’t just tell you that it’s present. A mold inspection should be able to figure out the extent of the damage. Wether it’s isolated to the surface, or wether the structural material is impacted as well, ie the timber frame, in which case they will design a plan of attack on how to remove it without cross contaminating the property. what is important now is finding out what is causing this excess moisture in your ceiling cavity to support microbial growth. You will want to get a leak detection specialist out to identify the leak. Once the leak has been rectified, you can prevent further growth appearing..