I taught myself bass and guitar with a few instructional videos and tabs, before the internet was a big thing. I wish I had had some of the information that is out on the internet then, it would have made the early days much easier. It is definitely doable.
I can't read music. I can fumble my way through tabs, but most of my learning is done by ear. It would be a huge advantage when learning a song, but not really necessary. I wish I had learned when I was a kid, it would be much simpler than now to pick up.