Judging from the title of your book and what reviewers have said about it, you should probably look for a different book. Contemporary jazz is built on an entire system of theory that differs significantly from the traditional system.
Jazz theory today is its own discipline - there is far more to playing good jazz than just applying "jazz licks" to a standard chord progression.
You should consider books such as:
Having said that, IMO, as an experienced musician your ears are your best guide, not theory or books - the theory is secondary. You need to listen to plenty of jazz, jazz played by the masters: Musicians like Louis Armstrong, Duke Ellington, Charlie Parker, Dizzy Gillespie, Miles Davis, Thelonious Monk, Horace Silver, Dave Brubeck, Charles Mingus, John Coltrane, Eric Dolphy... More than any theory, jazz is about feel and sound and timing - things that can't be learned from books.
Transcribing solos from such recordings is of great help in learning how it's done. You can also find transcriptions of great solo performances which you can analyze and try to play yourself - perhaps with a recording or drum machine, etc.
Also try to spend some time seeking out live jazz - preferably in clubs, where spontaneous new jazz is created on the spot, not formal jazz "concerts", a term which might even be an oxymoron.
With the sound of jazz in your ears, try improvising on familiar tunes - the traditional standards and even common every day tunes like Happy Birthday or Mary Had a Little Lamb provide great frameworks for jazz improvisation. You can find endless of good material for improvisation in a fake book, for example: The Real Book: Sixth Edition
Just play the tune and let your imagination kick in. I don't have classical training, but my understanding is that is often the most difficult aspect for those moving from classical to jazz: Learning to let your own imagination and musical instincts take charge, instead of just reading off the page and doing a bit of interpretation or following the conductor.
Although you are already a trained musician, if you're serious about playing jazz, also consider finding a good jazz teacher: Someone who will appreciate your already existing level of musicianship and help move you in the right direction for playing jazz. It doesn't have to be a lot of lessons - maybe only one or two sessions would be enough, just to "give you a push in the right direction".
You are very fortunate to be a trained musician that already has the basic tools at your disposal: Musical literacy and command over your instrument. Books certainly help, but ultimately using your ears and your innate musical talent will teach you how to use those tools to create better jazz.