I've been doing it for a long time. It's still not easy. Here's what I can tell you.
Early on, I had to just practice, practice, practice. Find a vocal/bass combination that is challenging you and just do it over and over. If you do it enough, you'll feel something click in your head that means you've gotten to the point where all the neurons in your head for doing this have connected and you'll have more independence between voice and hands. When this happened for me, I actually felt it and things were never the same again.
That being said, you'll still always have to do some work. Learn both parts, but get the bass part down to where it's automatic, because singing WELL requires a ton more concentration than playing well does. When you have the bass part down, you can layer the vocal on top of it and concentrate on making the vocal good. Practicing both at this point adds the polish.