I started on the bass last year, plectrum only to begin. Over Christmas I started experimenting with finger style (index and middle) and now it's my preferred method.
My bass is a four string Stingray and I anchor my thumb between the two screw arches on the top side of the single humbucker. Though I have no problems, I started to think about avoiding injuries and also the matter of string muting. I've tried the traveling thumb method, and I don't much like it, though I'd imagine it's essential if you're planning on a five-string (which I'm not).
Here's what I've settled on: my thumb anchored on the humbucker side-on (so the thumbnail's pointed towards the neck) with the base of the palm resting flat against the body contour. I've noticed that my ring finger is lending a hand with muting on the E & A.
It's working for me, just wondering how usual/unusual it is?