if you are willing to or fine with studying jazz at least, it should be fine. anywhere you go, most of the program consist of harmony, ear training, ensemble classes, history and private lessons. some schools offer more advanced or specialized courses like 'modal' harmony, 'advanced' ear training, 'artist' ensemble and on on.
once you graduate, you can be a freelance musician, which means self-employed or unemployed depends on perspective. there are tons of places you can work as a bassist like military bands, cruises, theatre productions and depends on where you are and who you know, you can teach bunch of people or even, will be able to become an instructor.
playing live gigs and etc. are great but in jazz industry, club gigs don't pay a lot. studio sessions do make good money but scenes are getting smaller and smaller. Neil Stubenhaus once said on the article of BP that if you are interested in becoming a studio musician, get a loan and build a home studio, then get some experiences and proofs. in 'pop' music, it's pretty much all business. if you can sell yourself, it'll work out regardless of your major.
depends on how you look at it, it's not that bad but you'd have to work your AXX off to make some quality living as a musician, at least in the beginning though. it gets better as time goes by since your work and all the stuff grows, too.
good luck with your study, hope you have great time during your school year. oh, GE sucks, man.