Re: Good jazz books
Failing the audition is probably the best thing that hapened to you because of the way you chose to rect: insist on getting better. We hae all been there and I am reminded of a quote from an interview with a UFC champion. He said that the way he looks at defeat is that it beats wekness out of you. This has stuck with me as an excellent context and I think you are looking at it that way too.
I recently picked up a nice book which will allow you to do some of the things suggested by the other contributors in the thread. It's called Baby Steps to Giant Steps and it is a collection of playalongs which go through all the tempos from very slow to very fast swing.
I have played jazz for many years but when I recorded myself playing to the first, slow track and listened back, I still found things I could improve an you will too.
And there is so much great information and, above all, encouragement from everybody here plus you have your teacher. You are all set!
Best of luck and keep telling us about your progress. If you can, post your playing so we can hear it.