In the previous examples the same bass note (the root note) is picked on the first and third beats. It is also possible to alternate the bass notes. This is a style commonly used in Country music. You can alternate between any bass notes that are in the chord shapes.
As long as you hold the chord shape while picking the bass notes it will sound correct. However, certain bass notes sound better with certain chords. The best notes to use are the ones that sound good to your ear. It is usual to pick the root note on the first beat followed by a different bass note on the third beat.
Use alternate bass note picking in the following chord progression. You can also experiment using different bass notes.
Rhythm Pattern
For the C, E7 and A chords alternate between the 5th string bass note and the 4th string bass note.
For the D7 and A7 chords alternate between the 4th string bass note and the 5th string bass note.
For the G7 chord alternate between the 6th string bass note and the 4th string bass note.
Practice each chord shape separately at first. Then try using alternate bass note picking on other progressions.