Your original question had to do with singing while playing the bass. None of the responses seem to address that point, so I'll give it a stab.
I also find it very difficult to sing while playing bass. I've been taking singing lessons for a couple of years now, and feel better about it, but still struggle. I'm a true amateur, so take this for what it's worth.
I think the two main difficulties (for me at least) are
- Singing 3rds & 5ths while playing roots. (With a guitar or piano, you're playing chords, so the note you're trying to sing usually is embedded in what you're playing)
- Singing off the beat while laying down a steady rhythm
For me, putting the difficulties in words helps, because I can then work specifically on the problem. There are many exercises out there to help you ID and sing 3rds, flatted 3rds, 5ths, etc., and with training and practice anyone can do it.
When singing, I usually can't play complicated rhythm patterns, but I usually can find a pattern appropriate to the song that allows me to sing and play bass at the same time. Likewise, I will look for bass line tones (notes) that will help key me into the melody tone I am trying to sing.
I don't know if this helps or not, but it's how I approach singing while playing bass. I'm still taking lessons, and I still hate my voice when I hear it recorded or on the PA. But I try to quantify exactly what I don't like about my voice, so I can work on it. (Right now it's depth and articulation, & my teacher's been giving me pointers to work on)
There are plenty of bass players out there who also are good singers that probably have better tips than me