My own musical education was initially rather narrow, focusing only on what was needed to get a big orchestra job. I think that narrow focus was in some ways a mistake, because musicianship is what sets a great player apart, and you can't get it by just practicing excerpts. When I was a student, there was a real division between those who studied the Rabbath techniques and those of us who were more "traditional." I was definitely a traditionalist as a student, but I've since had the chance to work with Francois Rabbath and I encourage any bass student to be sure to study both "methods." You can only add to your abilities by doing so.
My students at BW have a wide range of musical goals and end up doing many different things in their lives, from going to graduate school for bass performance, to touring China with a punk band to teaching in some of the most well-regarded public school music programs.
Your private lessons are the most important part of studying your instrument, obviously. You have 120 lessons during a 4 year undergraduate program and during that time, you must make the transition from being a student to playing at a professional or graduate level. It's really vital that you have a natural connection to your teacher and that you're on the same wavelength.
In addition to weekly private lessons, studio bass class is an integral part of studying the bass at BW and we vary what we study from semester to semester. Recently, we've focused on orchestral excerpts and mock auditions, studied bass pedagogy (comparing the Vance and Suzuki books), read "Casals and the Art of Interpretation" and applied it, and, of course, there are the infamous "scale semesters."