I have been the lead vocalist and bass player for a 60-70s rock and blues cover band for about 15 years. Before that I sang some background vox and a few songs lead in various bands over time.
It was hard at first and I could only do it on a few songs, and only then with lots of practice.
For me, the secret of success has been to let go. Once I started to just go for it, it got easier and easier. At this point, I can take on anything (vocal range permitting).
I will be the first to admit that my bass chops have slid a little and I tend to dumb down trickier lines to keep the groove and feel going.
My experience is that you can make playing mistakes or substitutions and most people don't notice. Screw up the lyrics to any well known song, however, and you will get criticized.
In the end, our audience likes it and the only people that know better are other bass players in the room.
Once singing and playing get comfortable, I find myself not actively thinking about either (except maybe when we are harmonizing and I cannot tell where the other guys is going to go).
Go for it and don't look back.