Music school is great IF you can afford it. Belmont has a great program-which I have a degree from, although it's very laid back, so there isn't a lot of pressure to motivate you; you have to kick your own ass. There are lots of other good programs around as well. University of Miami is very famously great, but there are more and more schools offering electric bass programs.
If you want to be a pro bass player, no one cares what school you went to when you audition, they only care if you're a good player and a good hang. You can get great instruction all over the place, the "big name" schools are better places to meet people, which is really more important if you're putting the time into playing. Belmont does have the great advantage of being in Nashville, and it's relatively easy to start getting work while you're still in school.
There are a few big points I would like to emphazise about my experience:
1. Music school is a great place to find out if you really want to play for a living. Belmont had about 450 music undergrads when I was there, and a lot of them ended up realizing they didn't want to play music for a living, but they love to play. They got their music degree and got jobs in all kinds of places-one vocal major I know loves his job as an event coordinator. They all still play around for this and that, but they have a degree from a liberal arts school that can apply to a lot of different things (can't say the same for a conservatory type "music-only" school, but they have their advantages-no one likes thinking about the big college algebra test when they need to be practicing).
2. If you're 1000% sure you want to be a pro musician, music school can still be really really great, but make 1,000,000% sure you can afford it-I definitely couldn't and went anyway. Here is the most important thing I can ever say on this board, and something no one ever went over with me:
I got every kind of financial aid (except academic, which I would have received, but wasn't available for transfer students), and still had to borrow an insane amount of money personally to go to school-how much? My loan repayment after interest started at $98,000 two years ago. No freakin' joke, I owe enough on school debt to own a pretty great house. $98,000 in my case translates to $780 a month in student loan payments, the average guy with my skill set and experience level in Nashville who is "making it" full time in music seems to be pulling in an average of about $1500-$2000 a month, which after a $780 student loan payment wouldn't leave me with enough to pay rent and eat etc. The bottom line-my student loan debt is why I am typing this reply on a computer at my day job in an insurance office-there's some hard numbers.
If you or your parents can afford it, that whole paragraph doesn't really matter much to you.
3. Lots of other ways to get a "college" level music education.
A. Move to a major city, find a high-level working pro, and start taking lessons. Add to that a good piano teacher, and a theory teacher (if neither of those is good enough in the theory department), and go to town. You can also find qualified vocal coaches, classical and jazz composition teachers around who will give lessons outside of a college. You can read about that all over major historical figures biographies-I remember one story about Mingus taking comp lessons from someone who had him transcribing Stravinsky-that is serious **** right there. Bonus: If you become a high-level pro's high level student, you will almost always by default become that high level pro's sub when that high level pro can't take a gig (note to self: 2 points for being gender-neutral).
B. Go to school for a while and drop out. Personally the path I wish I had taken. If I had gone to Belmont for 2-3 years and bailed out, I would have had most of the knowlede, made all of the contacts who I have gotten jobs from, and owed $25-40k less, which would really help, plus I would have been working more sooner and paying on those loans sooner.
It's great to finish a degree, but when your goal is something as non-traditional as a music degree, you have to take evertything in context. It IS pretty easy to go back to school later.
That's about all I think I have for now-better get back to work.