For years, I coud sing, or I could play bass. I could do these things individually quite well, but putting them together was a different story.
For me, it's all about subdividing rhythms. Learning which beats the vocal parts and the bass fall on. If you're just plugging straight eighths on a simple progression, you should have no problem since there's a bass note on every beat, but, once you start making it a bit more rhythmically complex, with gaps and different length notes, you have to start thinking about where the bass part and vocal intersect and diverge, and you practice the hell out of those bits.
Just to get the basics down, play ham-fisted, thumb around the neck, and use a pick since it's a bit easier to keep the rhythm. Then refine from there - put your fretting hand into the proper position, drop the pick (unless you don't want to), and start putting the gaps in, while keeping the vocal part consistent. Don't be afraid to look at the neck, but not all the time as your head won't be in a good position to sing (chin up, loosen that jaw!).
I'm not there yet, and I'm still far from Geddy territory, but I'm much better at it than I used to be, and this is what's helped for me.