One of the most characteristic techniques of fingerstyle guitar is the alternating bass. This technique uses the thumb to alternate between two bass notes, each played on a different string.
Although this is not easy, a steady alternating bass part could also give the player some grip during the learning process of a song, especially if the rhythm of the melody part is more complicated.

Exercise 1

Each note in this exercise is played with the thumb. Although it might be tempting to use more fingers than just the thumb, this is not recommended for now; as in more complex fragments these other fingers are needed to play the melody or the rhythm parts, it makes sense to get the alterating bass technique right by solely using the thumb.
Some players find it convenient to have their right hand its little finger rest on the first string in order to increase the stability of this hand.

Exercise 2

This exercise is a combination of an alternating bass and a walking bass. The low bass notes show only little variety, whereas a melody is played with the higher bass notes.
Many fingerstyle songs contain an alternating or walking bass part like this. Before including any other notes, like the melody, chords and perhaps percussive elements, one should first try to master the bass and play it with a steady tempo.

Exercise 3

The last exercise on this page features an alternating bass combined with a melody part.
A bass note on either the fifth or the sixth string is played on each beat, accompanied with a melody note. In between each beat a bass note on the fourth string is played. The melody notes are played alternately between the index and the middle finger, as is seen by the i and m above the sheet music.