3 in 1 isn't much different from 10W-30. And steel wool is definitely an abrasive capable of removing any finish on an instrument that I know about.
With all due respect to Rufus, I've known some real hot players that I wouldn't let get near one of my basses because of the way they do or don't take care of their own. Rufus' cleaning method would be more appropriate to preparing for a refinishing job.
What to clean with kind of depends on two things mainly:
1. the finish on your bass; oil, shellac, poly, or nitro.
2. the type of dirt on your bass, perspiration, general airborne grime, or sticky (beer, soda, etc.) or greasy (hand lotions, potato chips, etc.)
What you want to do is use a solvent that dissolves the dirt and not the finish. If you introduce an abrasive, you are not cleaning, you are polishing at least and removing your finish at worst. Use a cloth or sponge that won't scratch the finish. Most of the time if you have a water resistant finish (practically all of them), and there is no bare wood involved, you can get away with a damp sponge to get the water soluble dirt off. Most stuff that is just sticky will come off with water. If it won't come off with that, I use a touch of liquid dish soap on the damp sponge. If it won't come off with soap, then it ain't normal dirt. At that point you're dealing with something that requires an organic solvent like mineral spirits, alcohol, etc. Find out what kind of finish you have before using an organic solvent and make sure it is safe for that finish.
For fingerprints and general handling "skank" that shows up on glossy finishes (nitro, poly, some oil varnishes also) I like Gibson guitar polish in the pump bottle. Bioterra's Powerchord Skank Remover is another of my favorites for general cleanup. It works also for the metal parts and strings. For the raw unfinished fingerboard I have used #0000 steel wool and lemon oil, but other light oils (not as heavy as 3 in 1) work as well. If you like a waxier actual finish, Briwax is good choice for the FB, too. It wears off, but is easily renewed. The only thing I don't like about using Briwax is the toluene fumes. It's tolerable if you have the windows open and a fan going.