I tend to be a very modest person. I don't show any cleavage with clothes I wear. So I do prefer to cover up in public. I use this: http://www.cutiepoopsandbottoms.com/i_156/Bebe-au-Lait-Organic-Nursing-Cover.htm (baby shower gift!).
I can't discreetly latch her on. It's impossible. I nursed DD1 for 2.5 years but I dunno, my boobs are weird and tend to suffocate my children if left unattended. Lol. But if I'm with just women, I don't cover up. If men are around I do use my cover.