We have not played for a while, but I am the bass player and lead vocalist. I always found that simplifying bass lines helped. Above all, first you have to know both parts like the back of your hand. Funnily enough, quite complicated lines that "walked" around the fretboard tended to be less of a problem. It was when you had odd syncopation that I hit problems. Take the bass line in All these things Ive done" by The Killers for example. Dead easy bass line. But I could never play and sing it properly because of the odd timing of the bass in the verse. It stumped me and annoyed me for years. I got away with a simplified line and no one seemed to notice. I was however, very cheesed off that I couldn't get it.
I think the secret is, as it is with anything, practise, practise, practise.