It’s all about quality. It’s not enough to practice your instrument every day. You must have a quality practice session in order to better yourself as a musician.
What should you practice? You can never go wrong with scales (as boring as they can seem). Learning the fretboard is key to becoming a better bassist. You should know the placement of every note on your instrument.
Practice with a drum loop, or drum machine to help you get in the pocket, and stay there. What good is a bassist who has no sense of rhythm? No good at all. You must be able to develop a groove, and practicing with a drum loop will help you do that.
Expand your horizons. Just because you’re a rock (country, jazz) bassist doesn’t mean you can only play bass lines within that genre. The more stylist grooves you know, the better off you are as a bassist. A great book to learn stylist grooves is Bass Grooves, by Ed Friedland, and published by Backbeat books. It comes with a CD that demonstrates the different grooves. This books was a huge help to me when I was first starting to learn bass guitar.
Expose yourself. Listen to as many bassists as you can, both live and on CD. Other bassists aren’t your rivals. They should be your motivation and inspiration.
Take the opportunity to play with other musicians, especially those who are better than you. Playing with superior musicians will stretch you musically, and is one of the best ways to become a better musician.
Learn to read the bass clef (standard notation) or tablature (tab). You shouldn’t have to rely on reading music to play it, but it comes in handy when you’re learning new music or techniques, and is a heck of a lot quicker than learning by ear (most of the time).
Finally, don’t give up! The bass guitar is an incredible instrument, but most people don’t learn the bass overnight. It takes time, love, and dedication to be an accomplished bassist, but it is well worth the effort.