How much and what kind of playing are you doing now? Juilliard is gonna want you to play upright, their jazz program doesn't offer a course of study for bass guitar. Getting into the other schools is kind of a numbers game - how many bassists are applying to the jazz program, how many play upright or double and what's the skill level. If they only need 30 bassists and 300 apply, they're gonna look at the top of that heap. If only 20 apply, then everybody gets in.
The guys who do the best here, in school or not in school, are folks that can pretty much play a pretty high level before they get to NYC. Sure, there are more awful musicians here than anywhere else. But there are more absolutely wonderful players as well. Basically the best and most ambitious players from anywhere else in the world end up here. So you need to have an objective view of where you stand in that context - are you already playing pretty much all the jazz gigs in Manchester and the surrounding areas cause you're the first bass player everybody thinks of when they get a jazz gig? Or are you just trying to break into that scene? Have you been playing jazz for a bunch of years or are you just getting started? Look, NYC ain't going anywhere; you may be better served by getting to the point that you absolutely rule the local scene and THEN come to New York.
On the other hand, if you're OK with scuffling and doing other stuff while you learn, it's great exposure to what this music really is all about. I moved here almost 23 years ago with the idea that I was gonna stay a "few years", learn alla this stuff and then go back to Georgia and get all the gigs. I am kinda amused by that now, I can't really think what it would be like leaving NY.
READ a thread by
ROBIN RUSCIO here, he asks about moving to NYC and a lot of us have chimed in...