I am hoping to audition for the New England Conservatory Preparatory School Youth Philharmonic Orchestra on bass trombone (website found here). As you can see, this is a very tough ensemble to get into. I have to prepare a slow and lyrical piece, as well as a fast, technical piece. For my slow piece I have Lebedev's Concerto in One Movement. Would it be appropriate to do the Bourée 1 and 2 Bach cello suites as my fast piece, or should I generally play only pieces written for my instrument (Meditation by Hidas is my backup fast piece).
A Bach transcription is entirely appropriate for a trombone audition. If the audition requirements don't say anything that exclude it, I'd say that's an excellent choice, provided you can play it well!
One thing I would be looking for as an adjudicator of an audition would be how you adapt the breathing required for playing the piece on bass trombone to the music. Portraying your interpretation convincingly and confidently is essential -- this is beloved music, and no one wants to hear it done halfheartedly. That's perhaps one risk you run in doing Bach compared to standard trombone repertoire, but it's such excellent music that if you pull it off, it will make a great impression.