One thing you really have to do is listen... explore many different styles of music and just actively listen to the bass line and the way it interacts with the drummer and other musicians. And I mean MANY different styles. The bass off Led Zep II is quite cool to listen to, but you then also need to look how other styles use the bass (bring on the funk!). Remember, the bass is the rock for the other band members, you don't need to be a showman, be solid, keep the groove (especially the timing, but also be rythmical) and worry about the tricky bits later. (you can listen to music almost anywhere, good 'practice time' when you can't be with your bass as long as you pay attention to the music).
Playing with other people (once you have some basic chops sorted out ) will improve you no end, and quickly... as long as you keep listening! One ear for you, one for the rest of the band.
Once you have a reasonable understanding of the fret-board (i.e. from all the basic theory stuff you will learn by following all the advice given so far), learn the major scale and ALL its modes. (You can go on further from this later). Basically, you first learn the major and minor scales (which is the 6th mode of the major). Then once you have those two in your head, learn the 4th and 5th modes (each is only one note different to the major). Then all of a sudden you find that you know 4 out of 7, and that the following three are similar to what you already know! Knowing the modes really opens up the way to be able to jam with people and come up with a groove that is not just a rythm of the root note. Best way to learn the scales/modes? Learn a couple... THEN USE THEM! So by the time you learn the next couple, you already have a 'context' in which to remember the first two.
I get the train to work and on it I use a metronome (which happens to be on my iPhone
) to do timing excercises (tapping my leg with my fingers). There are a number of really good excercises you can do and since it is about having the timing on the inside, you don't need to have your bass with you! PM me if you want more details on that. (A good metronome will give a nice sharp noise on the mark, a cheeper one will give more of a beep which goes for too long and will not do you as much good, you want a suond likt a drummers rimshot on the snare)
Be carefull of watching/listening to people like Victor Wooten or Jaco Pastorius... you may get over-whelmed and give up! (Seriously though, get in to listening to those maestros, just don't expect to be like them without 2 decades of hard work!)
I could write all day... but just remember, learning the 'technical' stuff (notes, technique, scales etc) is important, but it is only a small part of the bigger picture.
Also, don't be afraid of playing with your tone knob and the position where you pluck/pick/slap/whack at. You'll get a lot of different sounds out of your bass. It took me years to 'find' my tone knob, it is good to play with one on a one pick-up bass so you can get a feel for it, (like a P-bass), when you have a tone knob for each of two pick-ups too early it may be overwhelming. Unconventional right-hand technique will create many new tones!
So where were we... oh yes. Learn the basics, listen to lots of different bass, and learn to 'groove'.
