Options include looking for discoloration on surrounding areas and even putting a paper towel or Kleenex in suspect areas in order to detect a small leak that may not have been sufficient to create noticeable discoloration. Depending on the volume, you may be able to hear dripping in order to help trace the leak. And you may wish to reconsider whether the initial diagnosis was correct or whether the repair was sufficient.
Here are three causes that weren't obvious to us that you may wish to consider:
(1) Around the tub spigot: We had a situation in which we had a leak from a bathroom on the ceiling of the dining room beneath it. We re-caulked the tub and shower surround, did a small test, didn't see any water leaking, and thought we'd taken care of the problem. The next time someone showered the leak reappeared. We eventually figured out that the problem was around the spigot: Water from the shower was hitting the spigot, and because there was not a good seal around the spigot, water was running behind the spigot, down to the floor, and eventually into the dining room below.
(2) The actual copper supply line connections--if you're fortunate enough to have access to them without tearing out the wall: In another house, one with only one floor, we thought we had a leak in our shower pan, but during a remodeling discovered that the hot supply line had not been soldered correctly and water had been squirting out between the wall and eventually out through the brick in the adjoining exterior wall.
(3) Diversion due to insulation: We had another leak that we thought was due to a problem with the flashing between the roof and adjoining siding. After tearing up the roof and the ceiling of the room being damaged, we discovered that the problem a poorly-sealed nail in the roof itself. However, this location was several feet away from where water damage showed up. In this case, the insulation directly below the small leak was sufficient to keep the water from running straight down. Instead it wound around and into another room.
There will be the potential for the mould to reappear as (as you have correctly surmised) there might be still some water in the ceiling space.
If you can, lift the floorboards in the upstairs room. This will allow you to see the extent of any damage and also get the air into help dry the patch out. If the area affected is not too wet then leaving the boards up for a while will help. If it is really wet then you might have to cut away the damaged board and repair the ceiling.
There are other questions here on how to patch a hole in the ceiling.
Best Answer
Plumbers putty is for specific purpose and may or may not solve the problem. You must find the root cause of the issue. You need to investigate and troubleshoot. it could be leaky faucet components, leaky tub shoe, leaky overflow pipe, leaky trim, etc. Remove all the faucet trim and run water, look in the wall with a flashlight. You made need to open the wall from behind or the ceiling from below. This very well be much more complicated than jamming putty everywhere.
If you do not understand the above and/or don't want to do some serious work... call a plumber.