So, here's my take on an answer to the OP:
I had EXACTLY the same questions when I started about 2 years ago. I began watching the original Flatt and Scruggs TV show tapes in Black & White to figure out an answer. I figured, if it was good enough for them, It would work for me. I also watched ever traditional Bluegrass player I could find on YouTube, and live. I watched and watched. I can summarize my results below in 5 simple stupid rules to make it sound like traditional Bluegrass:
1) If you possibly can play an open string, do it. It sounds better, and is easier on the Left hand
2) Always pick a 5th that is LOWERr than the root in tone, whenever possible.
3) Try not to play anything except Roots and 5ths except for an occasional passing tone or walk
4) Think about your bass the way a drummer thinks about his bass drum. Primarily you are there to keep rhythm.
5) Most of the time, the other players don't even know what notes you are playing, but feel your rhythm. If you mess up a note or two NO ONE will even notice - even if it is an egregious error, as long as you are playing in time.
Unfortunately, this is a very boring and unrewarding playing style for the bass player. But my experience, it this is what the traditional Bluegrass players crave and demand from the bass player. Some times I feel like a Baskin Robbins ice cream parlor where no one ever wants to buy any flavor other than vanilla :-(
If you do this enough, every damn song starts to sound and feel the same. I often find myself asking "Why am I even bothering to do this?" But its what they all seem to want. I get away from the boredom by listening to the other instruments and reminding myself how lucky I am to be enjoying great Bluegrass up close from folks I enjoy playing with. I also have learned to sing, and that gives me plenty to do.
OK, I'm having a really angry moment now - I'll just say it: Bluegrass Bass can be a totally thankless, mind numbing boring, back breaking, painful to the arms and hands, inconvenient, expensive, and unnoticed pursuit. Yet, I can't imagine giving it up. I absolutely adore it.
Why do we do this to ourselves??? The damn upright bass has somehow gotten into my blood like a space alien parasite on Meth. It hurts a lot both mentally and physically, but I can't seem to get enough of it.
Does that answer your question? OK, done ranting, going back to my disconnected fugue state in 3..2..1...