most moms i know pump anyway and bring a bottle or two with them whenever they're going out. no big deal.
i don't see a problem if like suddenly the baby needs to eat, just be discreet about it. since it involves multiple bodily functions (eating and...excreting, kind of), you should be just as courteous as you would if it involved anything else.
it's your personal business (your baby, your boob), but it's a shared space, so...
it's supposed to be a relaxing for the baby and is an intimate mommy/baby experience, so i don't see why a mom would want to do it in most public situations, anyway.