Nothing works better than getting right into it and trying to learn songs. It will take a while, and you'll feel like you're not getting anywhere, but you have to start small and build from there. I've learned that the best way to be able to learn something and play it by ear is to internalize that you want to play. The best way to internalize something musical is to be able to sing it, so we'll go through that method below.
Pick a really simple song, with a really simply bassline. Take any pop song with a definitely bass in it, for example. Play that song on something like Youtube, and try to sing the bass notes. Repeatedly start and stop a song to repeat a single note if you have to. If you not completely tone deaf you WILL eventually figure out what not it is. Repeat this until you have a progression down that you can sing.
Then, sing the progression to yourself and play notes on the bass that match what you're singing. Again, it will take some time but eventually you'll get the right notes.
Rinse and repeat for each progression in a song. I can't stress how this might take time but it's necessary.