Hey welcome! I've been playing bass in grateful dead cover bands for about 5 years now and I still have not fully figured out phils approach to bass playing. It kinda has changed throughout the years with him as well. Pre coke and booze years (68-74) the booze years (77-82ish) and post years all sound very different to me.
Most of the "essential" phil tabs are on the site and pretty accurate. (by essential I mean that he played that lick consitently night after night and you shouldn't really try and change it too much) examples of that are music never stop intro, help on the way, lazy lightning/supplication.
Start listening to shows and try and figure out what he's doing. He doesn't play the same bass line from verse to verse. He doesn't always hit a root note when bob hits a chord but sometimes he does. He can drive you mad. I play with the chords of the song sorta like a lead guitar player would using arppeggio's and different modes to give it a different feel. However you need to listen to the rhythm player and the drummer and try to use different voicings then both the rhythm guitar and lead player. Keep the beat don't let the group crash but don't become a slave to it. Or you will find yourself just strumming the root qutar notes. I have a real hard time trying to explain how I play things but hopefully this helps for something. the boss is here now gotta run.