Like others have said, it just depends.. on your natural ability, how fast you learn, how many hours of practice you can put into it per day, everyday (not time in months or years). After I was playing for a few months, I could play stuff that probably a lot of people couldn't play after a year - and that's because I put in as many hours in those few months as most people do in a year, like 4-8 hours a day, everyday. I just spent a whole winter learning tab for songs I like (mostly classic rock). And that was before the internet so I had to buy the tab books! We have it made as musicians now!
When I went to college, it forced me to have my bass in my hands a solid 6-8 hours a day for 4 years straight (and I played in various bands with friends along side of school bands). I really think I progressed several "years" faster than the casual musician would have (and it helps to be surrounded by great teachers and players all the time). I still try to put in 2-4 hours a day, everyday (whether it's by myself, practicing with the band, or gigging) because I love it. I feel like I'm missing something all day if I don't pick the bass up.
I think I was gigging parties and stuff within a few weeks of picking up the bass. I sucked, but nobody expected me to be great, it was just fun! You really just have to drop any inhibitions, and not care. I know that's easier said than done, but as soon as you learn to do that, you'll automatically look more confident on stage to the crowd. And that will draw the people in whether your hitting just roots or flying all over the neck. Smile and nod, and look like you know what you're doing. And just dive in head first!!