Agree with Mushroo and Jeff that the pieces are meant to be musical first and foremost; the technical aspect is just the means to that end. When I started studying the cello suites on the double bass, it was after having listened to performances by great cellists for years and having that sound and conception in mind. I would recommend doing some listening and finding inspiring recordings of whichever piece you are studying first, then diving into the piece with that sound in your ear. FWIW I don't find the recordings that come with that book very inspiring at all.
Once you have the sound in mind, try to imitate it as best you can on your instrument - the phrasing, articulation, dynamics, contour, etc. When you do this you'll find that there are a lot of places where your technique gets in the way. At that point, you'll know what to work on. I like to practice each new piece very slowly and choreograph the physical movements that make the music flow.
Good luck, and enjoy! This is some of the most beautiful music on the planet.