Re: Cleaning a floating bridge
After playing, I wipe down my strings with a rag soaked in 99% isopropyl alcohol (rubbing alcohol from the drug store). I make sure the rag surrounds the string and then wipe it up and down the neck. Do one string at a time. The strings literally ring out while doing this. It removes all the junk. I'll use the same rag to wipe don the metal part of my guitar to remove sweat, grease, crap, etc.
My strings will be corrosion free for months and I usually change them out once one breaks.
I wouldn't recommend any oil based product just because it will attract dirt.