One bass line that does so is the one from the song Wipeout by the Beach Boys. This line plays the root three times, a leading note down to the fifth played twice, and then a two-note leading sequence back to the root. Of this vast array of chords, only a few four-note chords are widely used outside of jazz, and I'm only going to talk about those chords. They're made by adding one more note onto a basic three note chord. The most commonly used four-note chord is made by starting with a major chord and adding the note 1.5 steps above the fifth.
Seventh chords are easily the most commonly used four-note chord.
You can also make a minor seventh chord, by starting with a minor chord instead of a major chord. Another note you can add to a major chord is the note that is one whole step above the fifth of the chord. This note is called the 6th note, and a chord that contains it is called a 6th chord. The most widely know song that uses it is probably Johnny B. Goode by Chuck Berry, but there are literally thousands of songs, in all keys, all styles and all tempos, that use it. The general pattern is known as the twelve-bar blues, and it's probably the most widely used song form in popular music.