I use what WayneS describes as the "floating anchor", and when I play my low B string (it's a fiver) I rest my thumb on the bridge pickup. I play a Fender MIM jazz, and it's pretty much the only kind of bass I've ever used frequently. I've become so used to resting my thumb on the bridge pickup...
Never Gonna Stop - Rob Zombie
Lessons - Rush
Shot in the Dark - Ozzy
Trademark - Eric Johnson
Just to name a few, the list of fun songs could go on forever :D
I'm somewhat picky. I try to get as close to "my sound" with whatever bass/setup I'm using. "My sound" changes all the time, though, so I guess I just think of the sound I'm looking for in my head and try to get the bass to sound like it.