Getting your name out there would probably first be achieved by establishing yourself as a great, reliable, flexible, cool to hang out with live side musician. Most studio people in LA come from that first.
+100 brojillian
I moved out to LA in 2007 and scoped all the guys around me who had a similar vibe like Kaveh Rastegar, Joseph Karnes, Nick Rosen, Edwin Livingston, Dave Wilder, Ethan Phillips. They certainly aren't the show off kinda guys you see in the r&B jams at the FEDERAL in the valley, but solid professional players who know where the bass fits. Hell, Ethan was the one who encouraged me to pick up an old Japanese knock off PBASS in Tokyo cuz it sounded better than the PBass I had at that time.
Get to know your fellow bassists and hang out with them too! Talk bass, drink beer!
The thing i learned from them, do the gigs, then hang out, always show up on time, be easy to work with, friendly, NO EGO.
I played by these rules, and started getting session work, then left the country for 3 years to propose to my current wife in tokyo, just came back to LA and lo and behold, people are calling me again offering me work.
Be cool, reliable, solid, and get to know your scene.
If you wanna play bass on film soundtracks, get to know the composers and the ever elusive studio session contractors.
Don't let people talk you out of it saying there are 1000 other bassists doing the same thing. 80% of them are doing something wrong anyway... (Focusing on gear, practicing that Pattitucci/Wooten/Myung solo, complaining about how there aren't any paying gigs)
Be reliable and personable and you'll get gigs filling in for your heroes like JMJ!
(I'm always one removed from JMJ and Flea...doh!

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