I always wash my quilts after finishing them.
I just quilted a top for a friend. Her great-aunt made it and it looks like 30's fabric. I think the backing she gave me to use is a poly blend. I used warm and white batting that I knew would shrink but she didn't want poly batting. Not knowing if the backing would shrink, I layed it out to dry istead of putting it in the dryer. I forgot to put the Color Catcher in-Yikes! But it all came out great! Phew! No bleeding and it looks so much better. Got rid of some spots on the top and brightened up the white background.
I have never prewashed batting but I know some people do to preshrink it. It shouldn't be necessary with the poly batting though.