Hi Cass,
big question that.
First thing to realise is that you won't get to be pro just by being good at what you do. For most people, if not all, who end up pro there's a fair amount of luck/grace/whatever involved, especially with regards to being in the right place at the right time.
that said, there are things you can do to shorten the odds on getting somewhere.
Firstly, I'd suggest getting your playing to a place where you can handle just about anything - be prepared to play as many styles as possible (therefor having the right sound for as many styles as possible), so that you never have to turn a gig down just for not being good enough. Listen to as much music as possible, and file away the salient points of each particular style somewhere in your head, for recall later on. One of my strongest assets in any musical situation is the size and scope of my CD collection - I've got a reference point for just about anything.
Next, go where musicians are. It may sound obvious, but hanging out at places where other musos hang out is going to help you get somewhere. Give up on any notions you have of there being any heirarchy in the musician world, beyond that imposed by security people...

- the guys you listen to are in just the same position as you, they're just doing more gigs. This works both ways - people who haven't done what you have deserve the same respect when you meet them as if you were hanging with Marcus Miller. So hang out with musos, swap CDs, tapes, and arrange to jam with as many people as you can. Feel free to be choosey if a certain situation looks like it's going to be a waste of time (jamming all weekend with 3 stoned talentless 17 year olds isn't being open minded, it's wasting time

) - but do take risks - you might find that some things are very cool that you thought were going to be a bit rough.
Linked to that point - have a demo of what you can do - put whatever you want on it, just make sure you come across as a pro. If you're looking at playing within specific scenes, then having a demo that reflects a knowledge of that style will help, but just sounding pro goes a long way. Photos and a bio are useful too if you're answering ads or working with an agency, but if some guy in a bar pulled out his press pack, I'd think he was a freak...

If he had a CD in his pocket, I'd think he was prepared.
Don't expect others to do it for you. If there are no gigs happening, think about booking some. If you're in a band, and can think of another local band that you could open for who are more established than you, look at promoting a show for them, thereby putting the work in to get yourselves out there. If you're putting on gigs, do it in style - contact radio, newspapers, mailing lists, get posters up everywhere. It's really worth putting in the effort, and gets your name about.
Take your demo into all the studios, agencies, etc. that are in your area. Talk to other bassists near you, get friendly and offer to sub for them. If there are long running shows in local theatres, then they may have a sub list, for guys who have learnt the show and are available to cover it (that's certainly the case in London) - if there are shows like that, and you know the guy with the bass chair, check out the music and see if you're up to it. If you are, get a copy and learn it. The exercise will be good for you anyway, and subbing on shows can be a cool way to kill dead time.
If you can teach, it's worth considering, but if you can't or don't have a 'calling' to do it, please don't do it just for the cash - it's tempting, but think how much it could have damaged your start in music if you'd had a teacher who didn't know what he was doing and resented you being there... teaching music is way too important a thing to do it badly...
If you've got your own band, contacting festivals is a good way to get your name about - festivals often have a built in audience, so are good for raising your profile, and as they book loads of bands, are often easier to get a set at than a local club. If you are gigging with a band, make sure you have a mailing list, and have the signup sheet at every gig.
keep an eagle-eye on any publications in your area that advertises musicians wanted/available - you never know what might come up.
Lastly, stick at it - there are no guarantees in this business (I know some incredible musicians who can't get gigs, and some dreadful ones making insane money), but you can shorten the odds on getting somewhere by playing great, being seen, and being the nicest guy that anyone you ever talk to has ever met.
The number one distinction between the A-list guys I've met and interviewed and those who are desparate to make it but aren't getting anywhere is attitude - Lee Sklar, Michael Manring, Jimmy Haslip, Abraham Laboriel, Victor Wooten, Steve Rodby and Doug Pinnick are among the friendliest most helpful open and supportive people I've ever had the good fortune to meet. All of them were grateful to be doing what they were doing, and none of them - at least in their time talking to me - showed any sign of being bitter, or overly competitive or nasty about anyone else in the business. That stuff goes a long way.
good luck - and wish me luck, we're all on the same journey...
Steve
www.stevelawson.net