First things first: your town...
If the people in your town aren't talking about you, then it's your responsibility to get out there and make sure everyone hears you. Make sure you're ready for this though... first impressions and all. Don't overstep or overstate your abilities. If your playing is worth talking about, the word will spread.So participate: jazz jams, blues jams, rock jams... whatever. Hit every one of them that'll serve as a good showcase for your playing. A good bassist is worth his or her weight in gold. Band leaders know that the key to a good band is a great rhythm section. Thankfully for us - with this instrument - the pool is shallower than say good guitarists. There are simply fewer of us, which makes our mission that much easier.
Get heard!
Be willing to bite it and work for crumbs at first. It pays off more in the end if you can get your name out there. Don't let those low paying gigs go on for too long though, and don't let anyone take advantage of your good nature. Know that you'll have to pay some dues but also never forget your value.
For me, when I was coming up I had a rule. It was this: Say yes to every gig if it meets one of these criteria:
Musically and artistically satisfying
Good money
Good exposure
A chance to learn
More than one? Bonus.
Basically, while I was trying to make a name for myself, it either had to pay, get me heard by people I wanted to hear me or, at the very least, be a lot of fun or challenging in some way that tipped the scales.
Be careful though, and don't work yourself to death. Be patient too, because you don't get to be "in demand" right away. That takes time to get that top pay and per-diems and all the rest. Be willing to work for it for a while.
Go to the shows and meet the other musicians with which you hope to be associated too. If you want to get "in" with the jazz guys in town, you should start going to their gigs. Meet them, compliment them, mention how you play as well and have been hoping to meet some more players in town. Ask - politely - if you might be able to sit in if the environment is casual and the vibe is right. Sometimes, it might just make more sense to wait and be asked.
Good musicians are always on the lookout for other good musicians, and most of them are pretty good at reading people. Don't just start talking about how great you are. Good musicians tend to have finely tuned BS meters, and one thing you'll notice is that the greats never need to talk about how great they are. It's usually the "wannabe's" who can't stop bragging about themselves.
In other words, be cool and be social. Don't go into overdrive with your sales pitch. Just hang, listen, appreciate and converse when the opportunity arises. Tell them about yourself and definitely answer all their questions, but also be interested in them and the group. Don't be that person... click http://www.linkedin.com/pub/rq-phillips/89/216/275/ to continue Working Your Local Music Scene.