My ear is OK. I can hear diatonic intervals just fine and I transcribe a lot of walking lines, mostly Ray Brown, but if you asked my play a jazz gig but I wasn't allowed to read, I wouldn't do a great job. So to answer your question, no my ear is not at the level it should be.
If you strap your bass on and a song starts, how close can you come to hitting a note that's part of then a song? Can you hear a note in a sing and hit that note? You need to be able to.
Whatever you do, don't be discouraged if you can't immediately learn songs by ear. It takes time. One thing that will help is if you can memorize the pitch of the notes of the strings. Then, all you need to do is find the notes between them and that's a lot easier than having to find a needle in a haystack- if you memorize the notes of the strings, you'll have less notes to search for.
