Since this isn't necessarily a question specific to Patrick Neher, it might get you more responses if you look into having it moved to another section. But since I'm here already, I'll chip in my thoughts for you.
For the world's most vague answer, it depends on the schools you're looking to apply to. For example, Juilliard's audition material is pretty specific:
- One movement from the Bach Cello Suites.
- A movement from the standard solo literature or the 1st movement of a standard concerto (Dragonetti, Vanhal, Bottesini, Dittersdorf, Koussevitzky) including published cadenza, if applicable.
- Two standard orchestral excerpts of the applicant's choice.
- One 3-octave scale and arpeggio of the applicant's choice.
Whereas some schools are quite vague, simply asking for "two contrasting solo pieces" which do not exceed 10 minutes total playing time. Many mid-level schools will require similar level music to the Juilliard requirements when it comes to solo repertoire. The first movement of a concerto OR a movement of solo Bach (referring to the cello suites) is a pretty standard request from what I've seen, although some lower-level schools will broaden the choices for the Bach requirement to be either a movement of Bach, or two movements of a Baroque sonata (Vivaldi, Marcello, Eccles etc). Basically, depending on the school you may have more leeway with the music choice, but what you prepare for a less competitive school may not be appropriate or even accepted at a more competitive school whereas what is acceptable at a higher school will oftentimes be just fine at a lower one, so make your choices wisely. If you're planning on auditioning at just some easier state schools, you could get away with some fairly easy music as many schools are desperate for bass. However, if you audition at more places you'll almost inevitably run into a concerto movement and/or baroque sonata or solo Bach as requirements, so I'd suggest choosing something that satisfies those requirements if you have enough time to get them down and can play them well enough, so that you're not limited by your repertoire choices when application time comes. If you're curious about what any school requires, you can usually google the school's name and "double bass audition" and you'll get some hits for the right page or at least a page on their site that can help you find the right one. There are also some compiled lists of audition rep for a bunch of major schools (I believe Jason Heath made one some time ago, try googling 'Jason Heath audition rep' and it should come up with his blog post). Of course you should always verify with the lists on the school's official page to make sure they haven't changed, but that can give you an idea of what some well known schools are requiring.
As for the difficulty of these pieces, if you're not already familiar with any of them, you can find almost all of them IMSLP for free. There's at least one version of all 5 of the major concerti there, as well as all of the solo Bach (granted, we bass players transpose some of the suites such as the third suite, and you can't find those transposed versions on IMSLP as they're newer editions. However if you picked something from for example the first suite, you can read off of a cello part as long as you transpose it up an octave, and there are cello editions for all six of the suites on IMSLP) and the baroque sonatas.
Your profile says you're just about my age-- are you currently a senior? If so, most schools have already had their auditions and started sending out their decisions (mine were all in February, and I only know of a few schools that audition in March or April, and their application deadlines would have all passed by now), so as far as I'm aware you may have to wait a semester or a year to be able to make the next round of applications and auditions unless you've already applied to some schools and could get in touch with their music department to schedule an audition in the very near future, which they might be able to do depending on the school. I don't know what level your playing is currently at or what solo repertoire you have under your belt, but if you could hack an audition with what you are capable of now, it might be worth contacting the music departments at any schools you've applied to to see if you can make that happen. Some others may have some wiser input on that subject though.
Auditions and audition prep are a nervewracking and stressful process, but if you keep in touch with your teacher and some other musical mentors, they can help to break down the overload of info that is available online so you don't go crazy trying to figure it out alone. Best of luck!
