I think the first time I've heard "Bernie's Tune" it was on bassoon, on Michael Rabinowitz' 1998 album "Rabinowitz in Utopia". Unfortunately I can't find very much information about that album.
Here's a transcription of the bassoon solo, transposed to B♭ and made to fit the trumpet ambitus.
You may download the music sheet as PDF, or in MuseScore format, so you can edit, transpose, transcribe and customize it to your own needs. Click the image to download the format you want:
learnjazzstandards.com, a great resource for whoever wants to learn jazz. There you can find a lead sheet with chord progression in concert C, B♭ or E♭.
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Cheers and happy learning,