I would do "Now's the Time" or "Billie's Bounce" . From my experience as an instructor at the Aebersold camp I can tell you what we look for and hopefully BOA has similar criteria. I picked those heads because they are bebop and include a few more notes than other heads so they can show off more technique and your ability to play in a swing style. good sound, good time, good intonation, then jazz style concept. The improv section would be to determine your level of understanding changes. Many beginners would just play a blues scale the entire time. Nothing wrong with that but a more advanced soloist might also include ideas that are more specific to each chord. Specifically on a blues one of the things that tells me the level of player is the second and fifth measures of the piece. When the changes move from the I chord to the IV chord. For example in Bb a player might play an idea in the first measure that includes a D. If the second chord of the piece is Eb7 (the IV chord) then using a Db in that measure would tell me that this player understands changes. Good luck let me know if you need more info on this.