I've played guitar for half my life, so I'm very comfortable singing while playing guitar. Singing lead while playing bass is a WHOLE different animal. I've only done it a couple of times. The most fun was singing and playing the bassline for CAKE's version of I Will Survive at a bar in SC.
Like everyone is saying, it depends on the song. It can be done, but it seems to take a lot more practice. Must be something about how bass rhythms typically don't match the vocal rhythm as closely.
I sing harmonies on a few songs in my originals pop/rock band. I hate the idea of dumbing down a bassline just to sing over it. I'd rather just practice until I could get it right, or ditch the vocal part altogether. But that's me thinking like a musician. If you're thinking like an entertainer (which you should be, if this is a cover band), and you think your audience will enjoy you singing the vocal part, the bassline can be simplified as much as you need it to be. As long as it still grooves enough to keep people's butts moving, you're doing your job.