Would something like artist management fall under the music business umbrella as well? What about studio management or something?
In any case, when I was doing my MA at NYU, my roommate was in their music business program. From the 'outsider' impressions I gathered through him, it's cutthroat. Even more so than the norm since the Stern business school is one of the best in the US, it's also one of the most cutthroat business schools. My roommate, who'd been in the cutthroat world of underground freestyle hip hop for a good while, was hip to that whole 'internal politics' thing and trusted no one in his program, but still managed to charm the pants off of everyone and used that shameless charming/flirting to his advantage.
I have nothing but respect for those who wish to go into music, be it music education, music performance, or music business. But one thing you need more than anything is a thick skin. Music educators need a thick skin given how art and music programs are constantly under fire at schools. Music performers need a thick skin for obvious reasons. Music business people need a thick skin also for obvious reasons.
If you're hungry enough, willing to grind your fingers to the bone for what you want in this dream, willing to both kiss ass and stab backs, perhaps even wh*re yourself out against your principles (i.e. take an internship at MTV even if you can't stand their pandering programming), even leaving a trail of abandoned 'friends' and broken hearts in your wake, you can do it if you have that kind of intense focus.