For "generic" taking care of leather, the DIY way, I wrote some longer answer here. Please feel fee to use the advice you find there, even though the object is different.
Shortly, this is what I would do:
- use some alcohol to remove dirt / grease;
- apply a thin layer of grease for leather ("paraffin oil");
- wait for the oil to permeate the leather, rub the excess oil with some cloth. If needed, gently use some alcohol-soaked cloth to remove excess oil.
If "deep" disinfection is desired, you may want to use a small UV-C lamp leave it on inside the bag for up to 30 min. Please search for businesses in your area; inquire about the smallest lamps they have.
If you use the lamp, be careful about these:
- it will get hot, and if the bag is completely close, it might break;
- if the lap gets any grease on the "glass" (it is actually quartz cristallcrystal), the lamp might again break;
The UV-C lamps, by design, use a small amount of mercury inside. If the lamp breaks, be careful not to inhale the mercury. You should use the setup in an area which is properly ventilated, to be safe in the case that the lamp breaks.
You probably already know this, but I write it for people who might not.
- clean all tools right after use;
- allow the tools time to properly dry before placing them back into the bag - especially the brush;
- make sure that there is nothing leaking from any of the tools, bottles; I had the experience with shaving foam coming as sprays. After use, there was always some foam expanding from the top, even after cleaning. To have the tube properly clean, I needed to repeatedly wash the top to get rid of the foam. In the mean-while, I switched to the more practical paste in a tube (similar to tooth-paste).