Bach and the Art of Improvisation Vol. I & II

This is a thorough book that discusses many ideas. I also liked the analysis of Bach's fugal subjects into a few standard phrases, which gives inspiration for one's own improvisations.

As has been pointed out by Timothy Tikker, this book contains a great list of historical sources, but it does teach improvisation very much as composition, and then gives little guidance how to get from composition to live improvisation.

From Pamela's website:

Bach's consummate musicianship through the lenses of musicology, history, theory, and performance. Improvisation pedagogy for professional musicians.

VOLUME ONE: Chorale-Based Works (2011)

1. Improvisation as Extemporaneous Composition

2. Tenacity, Touch, and Fingering

3. Thoroughbass and Cadences

4. Chorales and Harmonization

5. Counterpoint and Chorale Partitas 

6. Bach as Teenager: The Neumeister Collection

7. Bach at Forty-Something: Dance Suites     

VOLUME TWO: Free Works and Continuo (2017)

8. Interludes and Cadenzas

9. Preludes

10. Fantasias

11. A Thesis on Continuo Playing by J. S. Bach

12. Concerti, Cantatas, and Continuo Playing

13. Partimento Fughette

14. Bach for a Lifetime: Fugues