I have fronted a band for a while now as the bass player. I've done a Level 42 tribute and am now doing a Police tribute, as well as an original band before I get slated for doing the tribute thing.
Strangely enough some of the Police stuff has been more difficult to master where both are concerned, try Driven To Tears for instance.
Over the years I have found that it sort of feels like my brain has split into two, one for singing, one for playing. I still have to practice lots to master new songs but it gets easier as time goes on.
The best advice is PRACTICE. I usually learn the bass till I know it like the back of my hand, then the lyrics in the same vain. Then stick em together. It'll still sound and feel strange at first but it will come. If you are trying to read TAB or the lyrics at the same time this makes it much harder.
If you are doing original stuff just tailor your playing to the vocal line, that's what Sting did.
Good luck and keep PRACTICING.