Horological Meandering

Toothbrush helps too

 

I have cleaned many a filthy case and bracelet on watches sent in for servicing.

If the owner just wants things cleaned up, and it's a water-resistance watch such as a Rolex, we use a gentle soap, luke-warm water and a toothbrush.
Just don't flood around the pushers or crown unnecessarily.

More extensive cleanings are done by removing the bracelet from the case and cleaning it in an ultrasound machine for 30-45 minutes, then doing the soap and water routine.
Most multi-piece bracelets will hold enough dirt to blacken a quart of water.
And most of them will rattle a bit afterwards, since all the nice absorbent dirt has left the links to find a new equilibrium.
It's worth replacing the spring bars if they are ugly.

REAL cleaning requires more drastic measures, such as full disassembly for this Rolex.

Straps are a bit more of a nuisance and usually aren't cleaned.
I have had some success with cleaning leather straps using rubbing alcohol and then immediate application of leather conditioner.
It depends a lot on the type of leather and how much you've worn it.

Mike