There is an immense amount of solo and ensemble music for the double bass, as long as you know where to look.  I highly recommend every beginner start with the Vance Method.  In the first volume, the method presents the entirety of the bass in 6 positions utilizing familiar melodies in the lowest octaves up to the highest.  A variety of bowing styles and articulations are introduced.  Method Book 2 and 3 guide the student into more intermediate repertoire.

The Francois Rabbath method would be a natural progression to follow the Vance methods.  They are influenced by similar pedagogies.  The Rabbath method books presents solos and etudes which explore all positions, hones various bowing styles, guides the students through permutations of scale and rhythm variations.   A student who has studied through Book 3 will be on their way to being an advanced double bassist.   Book 4 and 5 are books which include many of his popular solo pieces.

If you need inspiration for solo or ensemble music to perform:

 here is a link to 4000 pieces of bass ensemble music.

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