Bass rhythm is often too different from the singing rhythm and my brain just gets confused despite all my best efforts.
This is the problem...
One solution is like zosoab70 said - foot tapping. That's it! well almost.
1) Play the bassline slowly while tapping your foot to the beat. Pay some attention to where the bass notes fall, relative to the taps. If you play with a pick (and singing and playing is possibly easier if you do), keep your arm going steadily up and down - may mean you will catch some notes on the upstroke. Practice this for a while until it's kind of automatic.
2) Sing the song while tapping your foot. again, perhaps a little slower than usual. pay some attention to where the bass notes fall, relative to the taps.
3) repeat 1) and 2) a couple of times
4) now bring them together. again, slowly at first. Tapping your foot, of course - the magic here should be that you are not needing to work out how the lyrics mesh with the bassline, because you already have in your head how each meshes with the basic pulse of the song (foot taps). There may be a couple of bits you still need to deconstruct - do this before you speed it up.
5) speed it up. May not be easy, but hopefully the gears aren't crunching too much.
So, rather than thinking of it as two things at a time (singing while playing), doing 3 things (tapping, singing and playing) might be easier...
...well it works sometimes.