IMO
a combination of things, a good teacher of course can help immensley at helping establish some good technique and guide you into music theory.
My first teacher was a bass player that doubled as a classical guitar player and gave me invaluable guidance on how to hold my hands and fingers and excersise that built finger muscle coordination.
And I agree that playing Roots, fiths (and I'll add 3'rd, and 6ths) will get along as a bass player. But the best advice I ever recieved was SCALES SCALES SCALES. Because becoming familiar with scales makes it so much easier to find the right Root, especially when the chord progressions get more complex then a basic blues pattern.
And it actually free you up quite and allows you to follow melodies easier.
And what I found is scales do not have to be dull boring excersises just going up and down and trying to memorize what note is suppose to be flat where. F..orget that!
You can use songs you know to learn scales, and how to hear/sound out the lines.
If you know the Sound of Music and the song "Do Re Mi" it cannot be beat to teach you the major scale. Because if you can sing that song, then you can sound out the scale, That is what the song is about. And corny as it may be. IT WORKS. I know.
I also recomment sounding out any childhood song you can remember. Because you know exactly how they should sound. It is just a matter of going slow when you need to, and really listening to the notes to figure out if the next note is higher or lower, and how big is the step (or interval)
I use Twinkle Twinkle Little Star, Mary Had a Little Lamb. Take Me Out to the Ball Game, Oh Susanna (Banjo on my Knee), and almost any Christmas carol/church hymn I can think of to sound out.
The reason is almost all of these songs are very basic scale based songs.
These songs should mainly be played by yourself "in the woodshed" where others will not be subject to your abuse, or your theirs.
The other thing that helps me most is playing with other people.
And that includes playing along with your favorite bands, the radio, the TV commercial, the soundtrack to whatever your are watching. Again, a practice best done in private.
I think you should put in time on your own, balancing fundamentals and finger excercises with playing along with your favorite CDs/Mp3s.
And balance that with finding people to play with. Preferably with people who are better musicians then yourself. (IMO)
And finally, my take on Tabs, and Reading Music. It helps, and you get out of what you put into it.
But that said, I think of the scales as streets, and on the streets there is cool music, if you can find it.
Written music is like a map and will show you how to get to those cool places.... but you still have to drive there. And you don't drive while staring at a map, you just use it to see where you need to go. And once you learn how to get there you don't need the map any more, and you might even find other ways to get there that are more scenic or avoids a tricky intersection.
So jam on my friend...
hope I didn't ramble too mcuh