I consider myself a professional user experience designer, and I have no idea. Please tell me when you find out. :(
UX as a discipline is still pretty unrefined: people are only just now realizing that you need actual (traditional) design (art, usability, ergonomics, cognitive science, psychology) skills to really do your job well.
A lot of people who call themselves web designers, user experience designers, user interface designers, information architects, interaction designers, etc., today, even (especially?) senior- or architect-level ones, are there because they were mucking about with HTML very early on, but they are often stuck in their current company because they don't have the modern skills we expect. They didn't keep up. They're grandfathered in.
Example: I interviewed people for a "web artist" position recently. I'd expect someone in that position to have good traditional layout, composition, sketching, drawing, coloring (whether painting or markers or Photoshop) skills, understanding of and practice using grids, typography, font selection, be able to describe their design process, how to run a critique, how to take a critique, plus a basic understanding of not just HTML, but CSS, and that they keep up on things like CSS animations and such. That's all on top of other things like demonstrated ability to work as part of a large team (jacks of all trades are immediately suspect) and being able to sit for long periods.
One person we interviewed stopped learning about the web when tables were okay to use for layout. One person couldn't articulate their design process. One person couldn't explain the difference between serif and sans-serif.
At my last employer, we talked about this huge list of knowledge domains that a UX person should know, how you need some theoretical or practical experience in all of them, plus depth in at least N of them. This came up a few years ago with the "levels of knowledge" lists:
http://friendlybit.com/css/levels-of-css-knowledge/
http://www.456bereastreet.com/archive/200605/levels_of_html_...
There isn't anything really like that for UX, although I've been sketching out ideas for one, coming out of the workshops I run.
The professional organizations are similarly disparate: IXDA is voluntary and (because of that?) I don't feel like it has a lot of ability to provide social pressure towards particular skill sets. Other organizations have narrower specialties: AIGA is for artists, UPA is for usability engineers, ASIS&T is for the information sciences, HFES is for ergonomics engineers, SND is for newspaper designers, SPD is for magazine designers... all of these organizations say they're branching out but I don't get the impression that any of them have any traction. That said, I also feel like I should be an active member of all of them.
In the short term, you might have the best luck networking within the media programs at art and design schools. I'd bet you were in the minority in your CS program, hacking on open source in your spare time. There will be a similar minority in the art departments, people applying their skills to web or games or some such.
Good luck!