The most common style of fingerpicking used in Blues is the constant bass style. This is achieved by playing a bass note with the thumb on every beat of the bar. This style is associated with Delta Blues players like Robert Johnson and Muddy Waters and more recently - John Hammond, Rory Block, Eric Bibb and Keb Mo’ as well as Texas Blues players Lightnin’ Hopkins and Mance Lipscombe.
It is most common to play the root note of each chord, although bass runs between the chords are sometimes used as well. The fingers play either melody or chords over the top of the bass notes. Melody notes can come from any of the scales you have learned, or from the notes of the chords played individually. Here is an example. Remember to use a metronome and be patient.
The next step is to play triplets with the fingers while playing a bass note on each beat as shown in the following example. Practice the right hand by itself on open strings at first if you need to.