Here is some detailed information on how to improvise on Stella by Starlight.
I have an entire book of Linear Jazz Improvisation chromatic targeting exercizes and etudes available to the public, entitled, Selma by Searchlight.
The melody of Stella by Starlight is its strongest component. Build your improvisations on a reduction of it, the guide tone lines and the root progression—all lines. While there are many melody notes which make ninths, elevenths, and thirteenths in their relationship with the chords, they mostly resolve in the fashion of late Nineteenth century Western art music, as opposed to the Twentieth century practice of leaving such tensions unresolved.
Don’t build your improvisations on the non-essential chordal accompaniment; it is even less important for that purpose in this through-composed piece (no repeated sections), since this tune never modulates from its primary key of Bb Major. If you feel you must think chords, however, there really are only a few worth bearing in mind, such as: the Ab7 in mm.8 and 21, and the G+7 in mm.17-18 and 24—all of which occur in prominent places, and contain chord tones that are chromatic the key.
The three examples below show Stella by Starlight’s Reduced Melody, Guide Tone Line and Root Progression. Internalize these by repeatedly singing and playing them on your instrument. Paraphrase, improvise on, and chromatically target them all. These skills will develop improvisational ideas organically. This process can be enhanced by chromatically targeting these essential compositional elements.