The bass guitar is a relatively new instrument. The instrument as we know it has only been around for a little over 50 years. I’ve been looking, but I still haven’t found a method that I truly believe in. My own technique is an amalgam of what I’ve learned from classical guitar and classical string bass.
As an ensemble instrument bass guitar needs to cover specific territory. Whatever style of music you play with a group the bass should be there with the root of the chord, on the one. If you’re not there, you better be doing something clever. If you want to be a really good bass player though, be sure to truly learn the instrument, every note of it. And I suggest approaching with the fingers of your right hand and not a pick. The pick is limiting and not really very useful.
For playing individual lines do rest strokes with your index and middle fingers alternating them like a classical guitarist. The first thing I would learn is lots and lots of scales. Everything you play will come from those scales. You can buy a book of “chords” for bass but this isn’t very useful either. You want to play intervals in the scales. Your most common interval will be the fifth (as the joke says: How many bass players does it take to screw in a lightbulb: one, five, one, five, one, five…).
If you’re playing a song and you’re supposed to play Amin7, the notes you may want to play would be A, E and G natural. These are the one, the five and the seven. If you see the chord E/G# play G# because the letter after the slash mark is the bass note. There’s a lot to study in music on the bass because although you don’t play as many notes as some of the other instruments you have to play the right note because you’re the foundation of the music. That’s why they call it bass.
One problem I see a lot of bass players having is that they hold the neck of the bass too low. I like to have the tuners above my head because this allows my left wrist to be straight. I get a lot more extension with a straight wrist, and therefore I can play much more interesting bass parts. It’s true that you can play bass with only one finger on your left hand if you merely play the root of the chord or the root in the fifth, but if you want walk the bass, you’ll need extension. I’m certainly not the only one who holds his bass up like this. Much of what I know about the bass is from watching Jaco Pastorius, and from a clinic I took once from Jeff Berlin. If you want to be serious about the instrument take a look at their music. They’re the best.