I think it's always a good idea to sing, whether you are good or not, or will do it in public or only in the shower. I'm an awful singer, but I'll continue to do it. Regardless of marketability, or ability, it makes me a better musician.
I can't think of a much better instrument for building your ear than your voice. You have no visual cues like frets or keys to work with, so you have to rely solely on your ear. Singing in pitch requires a good ear, and you can use that same skill for learning new tunes. Singing harmony requires you have have an ear for harmony, and being able to hear harmony and work within it can only help you come up with better bass lines. Singing background vox will help your ear for dynamics by helping you blend in with the lead vocals, and that ear can translate into your playing more dynamically within the mix.
I can't see any reason why singing would hurt. Even if you have a hard time singing and playing, by practicing it and overcoming it, you become even more fluid on the bass because it's more in your muscle memory. Then when you are not singing, it's that much easier to play the bass. It's almost like weight training.
There's a reason why lots of music schools require voice and/or aural skills to get a dregree. It helps you become a better musician. Even if you don't plan on singing, it's still a good thing to spend time on. And the great thing about singing is that you can do it anywhere and doesn't cost you anything, which means you can always practice and improve on your musicianship.