Bass and vocals is hard, much harder than the typical rhythm guitar strumming + vocals that a lot of lead singers get away with ... I don't know if this will help, but there's a trick I use when learning a new song on piano, which has a similar issue (right and left hands with very different parts). As per others above, learning each separately perfectly is essential: esp. with the bass, get to where you can play it without even thinking about it much - even go so far as to let your mind wander as you play. Then work on putting them together VERY slowly, to see where the rhythms of notes in each part line up and where they don't. Get used to thinking of yourself as either playing and singing notes at the very same time - which should be easy! - or playing and singing at different times - which should be easy! - then it's just combinations of the two - which should be easy!

Finally, and back to piano for a sec, when one hand is doing something more complicated than the other, I tend to look at that hand, but then still "hear" the other hand (that I'm not looking at) in my head. I'm not sure of the science of it, but it's like I'm engaging the visual parts of my brain for one and the aural parts for the other, rather than trying to do two different things with just one part of the brain, if that makes any sense ... In your case, perhaps looking at (or just feeling) the bass part, purposefully trying NOT to hear it (so it doesn't lead your vocals astray, which you mentioned is an issue), and hearing the vocal part, would work similarly for you and your brain.
Hope that helps, and good luck!