I know the obvious answer, "Practice, practice, practice" might seem like an annoying cop out answer, but it's definitely true of singing and playing bass simultaneously. But there are ways of practicing I've figured out over the years that have really helped me do both fairly efficiently.
I'm a lead singing bassist, so the more ingrained the vocal and bass parts are to the point where they become second nature, the easier it is to do, however, I've found that my attention is constantly flip flopping between focusing on vocals or focusing on bass lines, depending on the section of the song(s). While focusing on one part, the other may be temporarily on autopilot.
I like to break down the vocals and bass lines into rhythmic patterns and see where they fall and interact with one another. Remember the old step drum machines like the Roland TR707, where you could experiment with different drum beats and patterns by simply pressing or depressing the corresponding buttons assigned to those drum sections (kick, snare, hi hat, etc)? (Okay, maybe you don't, as I'm a bit older than some of you here). Well my mind kind of works like a step drum machine. I like to break down 1/4 note beats to 1/16th notes, employing the "1-e-and-a...(2)" approach to help count the accents in my head, meaning that within every 1/4 note of a typical 4/4 scale the vast majority of popular music will have 4 beats per 1/4 note, with the first accent on the down beat of each 1/4 note:
1st measure:
1 (down beat)-e-and-a (upbeat)-
2 (down beat)-e-and-a (upbeat)-
3 (down beat)-e-and-a (upbeat)
4 (down beat)-e-and-a (upbeat)-
2nd measure: (repeat pattern, and so on)
Somewhere within those 4 beats/16th notes per 1/4 note your bass/vocal notes will fall, so analyze if they fall on the down beat or upbeat (or both). Start simple with song/vocal melody you already know. Play a simple 1/4 note bass line under it. You can even stay on the same note just to practice getting the hang of the interplay of the rhythm of the lines in conjunction with singing. Step up to 1/8 notes if desired. Now start mixing up the pattern(s), perhaps 1/4 notes on the first 2 beats and 1/8 notes on the 3rd and 4th beats. Continue experimenting with rhythms and altering the rhythmic pattern of the line, working from that same initial 1/4 note, 1/8 note, or 1/16th note foundation. Perhaps 1/8 notes on the first 2 beats followed by 1/16 notes on the 3rd and 4th beats. Continue playing around with the rhythmic pattern of the bass line, altering or removing various notes. Maybe you continue 1/16th notes for the first 3 beats and on the last beat you silence the first three 1/16th notes and only play on the last 1/16th accent of the 4th beat (upbeat - "a").
From there you can experiment with more advanced rhythmic patterns - triplets, dividing the beat into 3, 6, 5, 7, etc parts (for 3/4 or 5/8 time sigs) etc. Again, I recommend just playing the same single note at first until the feel of different rhythms and placement of notes feels natural. And don't forget to take it slowly.
This book has been my bible for 25 years. I highly recommend it:
http://www.amazon.com/Rhythmic-Training ... 0881889768