here's my post from an older thread that I cut and pasted and edited:
I learned bass strictly by ear (I can read sheet music with other instruments but didn't learn bass that way). you do have to have a good sense of pitch. start by hearing or humming any note and then finding it on the fretboard. then build up by imitating simple riffs or melodies that you're hearing or humming. then focus on just what the bass is doing in a recorded song. and for gosh sakes, have a decent sound system with high quality speakers where you can play CDs etc. and actually hear the bass clearly. that helps to distinguish tones and pick out bass lines. small bookshelf speakers connected to the computer just don't cut it IMO. (it's like, why do people have to go to their car to see if their recording is mixed right? anyway...) I've spent a lot of time playing along to recordings. I'd go through it bit by bit pausing and going back until I get it. Now I learn songs off youtube on my laptop even though the sound quality sucks, but that's because I've been doing it for a while. and I would also say try not to look at sheet music while trying to learn by ear (unless you're with your band and it's in a pinch) because you're using a different part of your brain to process that different information.
also, see the recent thread on "playing along" in the general instruction section.