It seems everyone has their personal definition of what constitutes "modest" breastfeeding in public. There are the extremes of thinking it should only be done behind closed doors (I've even seen moms bf-ing their babes in public toilet stalls, ewww!) to the other extreme of exposing the entire breast, nipple, aureola, recent tatoos, etc, throughout the whole meal, even to switching sides, hello, where's a Nat'l Geographic photographer or Paul Gaugin when you need them?
I think we all should just try to be more considerate of others in whatever situation we find ourselves, and exercise tolerance towards the excesses of others as much as we can.
If you're a bf-ing mom, try to match your modesty to the circumstances around you. If you're alone with just your lady friends, you can let it hang out a little more freely than in a gathering with mixed company or alert children. If you're in a public place, try to gauge the temperment of the people around you. If you're having difficulty managing to nurse discreetly, practice in front of a mirror or a few close pals until you get your technique right.
Just personally, I found the moms who felt they must enrobe themselves with yards of covering fabric in order to nurse even among just women were being a bit too fussy & prudish. Or maybe they really had amazingly beautiful breasts that would make us all blind with envy if we ever got a glimpse of them.
Any time I tried to use a blankie to cover myself my nursing child would grab it and wave it like a flag to attract more attention to ourselves. I learned how to neatly and discreetly cover my babies and my breasts with my baggy shirts and no one ever knew I was nursing. I became skilled at nursing even while walking through stores and standing in the checkout lines, even briefly considered forming a marching troupe of lactating mothers. Sometimes at church someone would see me standing and holding my baby and reach out to take him from my arms to admire him and I'd have to tell them "not right now, he's nursing." They had no idea, it didn't show, it just looked like he was reclining in my arms.
Of course there are still some folks who have issues with any form of bf-ing in any public place, discreet or not. I know that at least in my state of Florida we have a legal right to publicly bf, but certainly not like a Tahitian islander.
I am familiar with your circumstances of sharing PCs at the library, and encountering the noise & distractions from fellow patrons & their lively children. (My personal favorite worst distraction are the folks who must talk to themselves or their computer screens while they work) Hotwings, I don't know if you are a man or a woman. If you're a woman, perhaps if you encounter another indiscreet bf-ing mom you could just politely mention that she's showing too much of her wares to the public. (And get ready to duck) Some moms will thank you nicely, some will get really defensive & mad. If you're a man, perhaps you should play it really safe and just tell a lady librarian about it.
If that doesn't work, get the atlas or some other big book, or get a stack of books, and make yourself a privacy wall. Or wear horse blinkers.