When I first started playing bass 15 years ago, I really had no knowledge of music theory or notation. I knew I had to learn it, but I really was dying to be able to play some of my favorite songs right then and there. I purchased a few books on theory and notation, but I also picked up a Rage Against the Machine bass tab book. That one really got me going fast. Granted, bass tabs, and all tablature in general, don’t indicate certain helpful things, such as the duration of the notes, but only after a few minutes of listening and tinkering around, I was playing the song “Killing in the Name”. I’ve been hooked on bass tabs ever since. It wasn’t until years later that I dusted off those books I originally bought and finally learned standard notation. I’m glad I know it now, but I rarely use it unless I’m officially charting music.
Eventually, I reached a point, like most well-practiced musicians do, where I didn’t need bass tabs, sheet music, etc, anymore. I can now just listen to the song, and pick up exactly what is being played with minimal problems. However, I’m not a musical genius by any means, and there are still times when I’ll hear a bass fill, or interesting, “notey” bass line that is quite tricky. If I can’t figure it out by ear, you should bet that I’m going to look up the bass tab, and not the sheet music.
I guess the point is that unless you are planning on being a studio musician, composer, or something like that, you really don’t need to know standard notation. Bass tabs, and all tablature are easier to read, and can help get you to a pretty high skill level. However from my experience, once I fully learned theory and notation, things really opened up for me, and I felt good about being a well-rounded musician. There will always be a special place in my heart for bass tabs though!