If you want to develop comfort and ease with changing keys swiftly, then practice patterns on the circle of fifths. In particular, work on dominant seventh chords; doing so will help you to develop facility in voice leading from the seventh of one chord to the third of the next, and vice versa.
The exercise on this page is one of countless possible dominant seventh patterns. I like it because it brackets the chord root with the flatted ninth and raised seventh, then descends from the root through the lowered seventh to the third of the ensuing chord. Bottom line: you get a nice combination of color tones and harmonic motion. Click on the image to enlarge it.
This is a pretty straightforward exercise, and I don’t think I need to say anything more other than, memorize it, apply it to the full range of your instrument, and have fun!
Oh, yeah…and, check out my jazz page for more exercises, solo transcriptions, and articles of interest to jazz musicians.