Although it is possible to play chords on the bass, it is more common to play the notes individually as part of a bass line. When the notes of a chord are played one at a time, they are called an arpeggio. The value of arpeggios is that they enable you to play lines which fit chord progressions perfectly, since every note of an arpeggio is a note of the accompanying chord.
The following example demonstrates a C major arpeggio which consists of the notes C, E and G. These are the root, third and fifth of a C major chord.
Here are two common arpeggio patterns for any major chord. The first diagram shows the Root, third and fifth, while the second diagram shows the repeat of the root note an octave higher. They are shown here beginning on the fourth string, but can also be used beginning on the third string.
Once you have the correct notes for a chord they can be arranged in any order. These various arrangements of the notes within a chord are called inversions. For example, a C chord could be played C E G (called root position), or E G C (first inversion), or G C E (second inversion).
The use of inversions opens up many new fingering possibilities all over the fretboard. It is worth learning all inversions of each arpeggio, as this enables you to identify all the degrees of the chord (called chord tones) more easily, which means you can respond quickly to what is being played by other musicians you are playing with regardless of the harmony.
If you know the notes and inversions of chords well, it also makes it a lot easier to improvise your own bass lines in any position on the fretboard. It is also recommended that you learn at least a bit of basic keyboard or guitar so you get used to hearing the sound of all of the notes of chords together instead of one at a time. Most of the great bass players also have an excellent knowledge of keyboard harmony.
Because it is the role of the bass to provide the bottom end of the sound of the band, it is usually best to stay on the lower part of the neck, or at least on the lower strings, for most of the time. If you play too much high up on the neck on the first and second strings, the sound gets thin and the punch of the bass is lost.
Remember that the bass is a foundation instrument, providing the drive of the groove and stating the basis of the harmony of a song. A useful technique for enabling you to stay in one place lower down the neck is the use of "upside down" arpeggios. This means that you go down from the root to the third instead of up, as demonstrated in the following example.