I would recommend learning theory, or more specifically, scales. There are hundreds of scales bassists must know—major, minor, harmonic minor/major, pentatonic minor, etc. Pick up a scale reference book at a music shop as well as a finger technique guide.

I have played bass for years and have found I learned the most from learning to play along with the best. It was a backward way to learn scales etc. I agree with @Vortico that learning finger technique is important as well. I have taken lessons etc but learned the most from putting a tune on and learning the part (every note). Some are melodic (Leland Sklar) on James Taylor songs, some will teach your hand to move (Doobie Brothers, Listen to the Music), some stretch your imagination (Theme from Thirty Something), some expand your sense of technique (Theme from Seinfeld).

Start with the basics. Find a good bass guitar instruction book. The one I have used and recommend is the Hal Leonard Bass Method. There are three books: Book 1, Book 2 and Book 3. Start with Book 1. And get the book that has the CD with it. Playing along with the CD while reading the notes in the book is the best and most motivating way.