Somewhere in the bowels of the Alembic Club, this info is floating around, but I'll repeat my 'Hints from Heloise' cleaning tips:
As mentioned in a preceding post of mine above, BreakFree CLP is the stuff for things you want lubed but not sticky, oily, or tacky afterwards. Harmless to finishes and electronics, a little goes a long way, and unless you're playing in a metal band 6 nights a week in very messy environments, it may never need any again . . . . . BreakFree also seems to 'sweatproof' things a bit, not a bad thing.
As far as the non-clear-coated brass (usually everything except the s/n plates and tailpieces), you can obviously used ultrafine steelwool (and this is better with it off the bass) on the bridge. I've also used car wax (and make SURE it's wax and not 'polish' or 'wax polish' as that has very fine grit in it to cut slightly), or if you score a badly neglected, all-green-crust older brass, Eagle One Wadding Polish is the court of last resort, it will really eat that stuff. I've never been a Brasso guy I'm afraid . . . .
I prefer the car wax as it really brings the brass to a mirror finish after the steelwool, if you like that look on the bridge and adjustable nut. Car wax is also great for getting fingerprints out of the tuning key buttons. And remember, don't even think of using any of the brass polishing stuff on plated items like the keys: You'll go from gold to chrome keys THAT fast, DON'T do it. I prefer Meguiar's for waxes, etc. And another reminder: Be sure you get straight wax, not 'wax polish' or any similar product that has any grit whatsoever for very fine cutting a car finish that barely needs serious detailing: This will leave marks.
So how do you keep the brass looking new, if that's what you want? Buy a tube of Alberto VO5, the old-school hair dressing in a toothpaste tube. Ease just the thinnest coat over the bits (and you can use this on the keys as well, it's harmless), and this stuff will keep it shiny for a long time.
If you have a gloss finished axe, again, I prefer Meguiar's, and use their 'Ultimate Quick Detailer' and 'Ultimate Quick Wax' (both in tall, Windex squeeze spray handle bottles), from Auto Zone, WM, wherever. The Detailer cleans, and the Wax makes 'em shine my-T-fine, unless you can score some the Alembic Supreme Polish.
And of course, to honor their heritage, a final step: Drop a drop of patchouli oil in an out-of-the-way corner inside the case. Somehow, it just seems appropriate, and the Police aren't interested . . . . . .
And a been there / done that tip: Be smarter than I was. I took the bridge COMPLETELY apart to clean/lube/adjust everything, and I re-installed it . . . . . . BACKWARDS, which I didn't realize until after it was re-strung. Duh-Oh!!! So take a few cellphone pics as insurance if you do this, and this will give you an approximate location for each saddle so re-synching your harmonics won't take near as long.
Life is Good !