I sing and play bass in my band. At first I would just do basic bass lines but now, the harder the bass line the more I enjoy learning to sing and play.
As a generalisation (for any song):
Absolute minimum - just sit on the root when you sing.
That's the starting point. That isn't hard to do - so start by adding the obvious. Go back and fourth between the root and the 5th on the beat for example. Or vary the rhythm while sitting on the root.
When you get that down play up to the 5th. So play Root, 3rd, 4th, 5th or something.
Everytime you play and sing each song - do something new and sit on it until you can play it well and then add something else new.
Before too long you'll get stuff under your fingers and be able to just play through stuff and sing comfortably.
The more you do it - the easier it becomes for each song.
For specific (really hard songs):
Break it down note by note if you have to and think of your voice and the bass as the one instrument. Like a drummer has to between hands and feet. ie it's about co-ordination and dexterity.
Slow everything right down (practice just bass and singing with nothing else) and sing/play it all note by note, part by part until you can play through it slowly. Then just play, play and play until you can get through it at full speed.
Then you take it to the band and play it in that setting. Hard at first but over time (weeks/months) you get it under your fingers and will get to the point where you can play really complicated bass lines and sing to the point where you can start mucking around with your phrasing whilst singing while your hands just do what they want to do on the bass.
I find it really challenging and a lot of fun - especially with the more complicated stuff.
And to be honest - it's something that can blow people away. ie it's a bit of a party trick - but also a very usefull/practical one.
I have had people come up to me after gigs and say they watched me the whole night cause they couldn't comprehend how I can sing and play like I do at the same time.
That's pretty cool considering I'm not the lead guitar player!!!!
