Hello I hope I can put your mind at rest.
The fuse box itself is not dangerous as it is protected by its own fuses. What I surmise has probably happened is that, as you say the ceiling lamp holder is on the ceiling under the bath, There maybe water that has got into the holder and shorted the circuit out.
The lighting circuit is protected by its own fuse which is the one that keeps tripping. I suggest that you take off the bath panel and have a look to see if there is any water around under the bath. Also with the lighting power off unscrew the ceiling rose and look there. If there is water try drying it out with a hair dryer.
But please if you are not confident in doing this, It maybe prudent to get an electrician to test the circuit out. This is for your own safety and well being.
I hope that this advice helps you to solve the problem.