Study the patterns for an 8-bar blues progession and get familiar with the chord changes. Blues chord progressions follow the same chord pattern, regardless of the key, and are notated by Roman numerals. A common 8-bar blues pattern is: I / V7 / IV / IV / I / V7 / I / V7. This means you will play eight bars based on the 1st, 5th, and fourth chords in the scale, with the fifth chord being a seventh. In the key of C, these chords would be C, G7 and F.
Build your bass lines over this chord progression by playing patterns based primarily on the notes in each of the chords with "blue" notes thrown in for feel and effect. Flatting the third, fifth and seventh notes of the major scale gives you the "blue" notes and creates the blues sound.
Familiarize yourself with basic music theory. This doesn't mean you need to read music, but an understanding of how chords are built is helpful. A major chord use the first, third and fifth notes of the scale you're playing in. A minor chord is the same, except that you flat the third to give the chord its "minor" sound. You can purchase a basic music theory book at any music store or online for a deeper study of this theory (see Resources).
Listen to as much blues music as you can. Try to play along and mimic what you hear. Many blues bass players (as well as guitarists, harp players, and piano players) improvise. Blues uses many of the same patterns, and over time you will begin to hear them and imitate them easily. The more you play along with recordings and other musicians, the better your skills at playing the blues will become.
Master the walking bass line. This is a pattern of notes, primarily scale and chord tones, broken into equal note values (usually quarter notes) and played with a blue chord progression. This type of bass line is common in 8-bar blues and creates a "walking" feel.