Work on the basics.
Scales
Arpeggios
Chord tones, walking lines
Rhythms
There are lots of books out there and teachers that can help you. If you have teachers in your area then I highly recommend you do a few lessons at least.
And play with others, always play with others.
And listen listen listen to as much varied kinds of music as possible.
This is sound advice. There's no magic formula for getting better. A lot of it is just putting in the boring study time.
Other than just practicing, my thought about the best way to get better would be;
1. Practice with a metronome. Even seasoned and experienced players use them, all the best players I know use them frequently when playing alone.
2. If you haven't done so already, learn basic music theory. If you know what notes make up chord tones, you can add some nice accents to those roots. A good place to start is learning the relative minors of those major scales. Practice and learn your scales, and if you are pretty proficient with basic scales move on to modes. Don't tackle modes unless you have a good understanding of the standard scales first because it can be a little tough to wrap your head around it (it was for me, and still is, as I don't know some of them without having to look at a sheet of paper).
Make sure your basics and foundation are solid. Everyone would love to be a Jaco, Geddy, or Victor, but for many of us (like me) that's not realistic. However, playing an instrument is much like building a house. If the foundation is not solid and correct, what comes after will never be right.
If you are self-taught, I would strongly recommend taking a few lessons on technique. When I decided to take bass lessons (from a competent instructor) after playing for a little while, I found out that some (okay, A LOT) of my technique was flawed and was partly responsible for my inability to progress faster. I had to learn some things from scratch, but it was time well spent as a few alterations to my technique made huge differences in my playing.
Try playing songs you wouldn't normally play. Don't pick real hard ones, but pick ones that have simple chord progressions but emphasize tone, nuance, and style. One that comes to mind is Lee Greenwood's "God Bless The USA". In the last band I played in I could pound out Travis Tritt's TROUBLE like nobody's business, but struggled with God Bless The USA. I always found slower, simpler songs more difficult to play but learning them and playing them made me a more tasteful player. People think it's cool, but in reality pounding root 1/8ths all the time actually covers a whole lot of sins, especially if you struggle with rhythms. Trust me, I know this first hand.
But it's all about getting that good foundation. You won't fly to the moon if all you have is a bicycle.
Good luck, and never give up.
