Congrats on your start in the studio world.
Gear: What everybody else said. While I believe that every working bass player should own a good DI, any studio worth its salt will have several from which to chose. That's it, really. The engineer and/or producer just want a good, clean bass track. All of the "sizzle" will be added later – usually without your artistic input – via compression, hardware/software effects, reamping, etc.
Skills: So as not to omit the obvious, as a session player, it's assumed that you can sight read – not just standard bass clef, but also alternative charting methods like the Nashville number system. Not every singer-songwriter is going to take the time to sit down with you on acoustic guitar or piano and say, "The verse goes like this, the chorus goes like this, and then there's this funky thing on the bridge..." Also, diplomacy is key to success. As an independent contractor, know your role, and don't bite the hand that feeds.
Best of luck.
