I find transcribing songs and then applying what I've learned to be more effective.
Same here. And like the OP, at the very beginning of me playing bass (I had a year playing guitar already) I still sucked at even finding the individual notes and root notes of chords, and such.
I thought I was destined to be enslaved to tabs forever, even when I learned they are largely inaccurate. Also, because of this apparent lack, I was truly scared of even attempting to transcribe any easy song. So I was playing off tabs for most of my first year.
The very first song I actually transcribed was "Fire" by Jimi Hendrix... and once I did, I checked the tabs, and we had the same notes (meaning, I could actually do it). Even with that, I still wasn't eager to just go for ear training full-blast. A few more months passed and I was still learning songs with tabs.
Then, all of the sudden, pam. I found myself wanting to just give it a shot. To learn the songs by ear. Now, even if I know I can't nail the song completely, and can miss a few things here and there, I'm realizing I'm not so bad at it, when it comes to hear the notes, and even the key, of a song. At the same time, I'm not paying attention to any tabs, and if I need a reference, I prefer to use chord charts instead.
And I can't say I'm a very experienced musician (2 years under my belt is definitely on the rookie side), but I am doing my transcriptions with easy songs. Whenever I feel ready, I will start with harder songs.
I say, just give this a shot, and if you make mistakes, it will only help you to start recognizing common chord progressions, intervals, and such. Heck, even some fills aren't that hard to figure out once you have the backbone of the song nailed. If you think you still can't do it, give yourself time, and try again when you feel the urge.