I'm still only fairly young but my take on reading is that it's not as important as getting your ears together, which I honestly think is infinitely more important. Every good musician should have a good understanding of harmony, melody and rhythm, if you can read then great, you'll get a lot of work doing it, but it's not the be all and end all.
However... there is no doubting that the likes of Nathan East hasn't got by all these years on just ear training. Most of the big session guys like Will Lee, Nathan East, etc. can read like monsters, mostly because they've come from a classical background and then moved onto bass playing. Freddie Washington in particular is supposed to be more or less unearthly in this department. Pino Palladino is quite the opposite, saying he gets by more using his ear having never been a great reader, which is equally admirable.
So it's probably not everything to be able to read... but it would help to learn if you want to be a serious player.