| I'm not a master, but after watching a lot of bassists, I'd say you're gonna see a lot of variation in fretting approaches. I've tried to carry through most of what I learned on guitar -- thumb on the back of the neck, fingers arched up over the unused strings (as opposed to laying across everything)...etc. The one thing that I've been trying to do more of is fretting half-ON the fret itself. I normall fret like on a guitar -- right up to the fret, but not touching it at all -- for a clear bright tone. But I started liking the lightly deadened quality a buddy of mine gets by hitting almost completely over the fret. I've seen guys who use their index finger as much as possible, moving the whole hand around to get to different frets. Personally, I try to use a finger per fret. But I'm a novice, so I still have places and songs where I don't always use the same finger in the same place -- it's like I'm still not quite comfortable with how I'm playing a particular phrase.
So there are mechanical considerations -- e.g. does it work well, are you comfortable playing that way, can your muscles take it -- and there are stylistic considerations -- for example, if you use one finger, your notes will rarely extend over subsequent notes (each note change kills the note before it), so the bassline will be more punchy or bouncy, whereas using chord forms where possible will allow you to let notes ring on for a while as you play later notes. And, in reality, at different times you're going to want different effects, so if you can toy with doing both, it'll be good for your arsenal. (and if you play finger style, you have the ability to kill notes with the follow-through of your other hand's strikes, so that's another way to affect the sustain of your notes)
cheers!
ltt | 
