As an LDS woman, I believe very much in dressing modestly. I also believe that breastfeeding is the way God designed for babies to be fed, and that the only way to make breastfeeding normal in our society is for people to see it. I believe that the negative view of American society of public nursing is a big factor in why women in America don't breastfeed longer. I have experienced firsthand the crushing isolation that results from trying to breastfeed in private as much as possible, as well as the frustration from trying to nurse a baby under a cover who didn't want her head covered up. So now I nurse in public. Without a cover. I do however, usually wear nursing tank tops (I buy them at Target) under my shirts, which allows for minimal exposure of my body while nursing publically. This is what I am comfortable with and what works for me, which may be different for different people.
I have put together this collection of blog posts from LDS women, sharing their own opinions of the issue of modesty and breastfeeding: