It's important to note, though, that learning to sing while playing will make you exponentially more valuable in any band situation. I contract a lot of musicians for paying gigs and I would take an adequate bass player who sings over a monster bass player who doesn't every single time. Matter of fact, from my perspective (as someone who writes checks to musicians), if you don't sing, why even bother playing bass? Because there are guys who do sing and they'll always get the gig over you. Amazing instrumentalists have a very, very limited appeal- mostly to other amazing instrumentalists.
I developed this skill because, luckily, my two earliest influences were Paul McCartney and Sting. Those were the songs I was really most interested in learning and most motivated to practice. My advice would be to find someone in your personal list of favorites who sings and plays and then shed that like a mother. It takes years to do well, but your big picture musicianship will expand greatly.
Not sure if this helps, but a piece of advice I picked up from Sting: think of the melody and your bass line like two train tracks that run parallel but expand and truncate throughout the song.
+1000.....Its going to take practice....when you are in the shed, I would suggest you start at a very slow tempo...as slow as YOU need to play the notes and sing the line...you may find it very very slow but after you get through it a few times...you speed up until full speed.
Here is Mark King (level 42) who makes singing and complicated playing look like child's play!
