I think after doing it a few times, you just kind of get over it. I had a nice breastfeeding apron at first, but that got lost somehow, and after that I would just feed in the car if we were out.
But when she was 7 weeks old, I had to take a plane to visit my parents, so I just bit the bullet and fed her right there on the crowded plane. I noticed that the guy sitting next to me very quickly struck up an animated conversation with the person on the other side of him, so he could turn away from me (same exact thing happened on my return trip, so it wasn't just my imagination).
But after that, I was ok with feeding in public if I absolutely had to, but of course I still prefer the car or some out of the way nook so I don't make people uncomfortable. I honestly couldn't care less who sees my boobs anymore, except for the fact that other people get uncomfortable.
A loose baggy shirt really helps; I usually wear one of my big maternity t-shirts if I know I'll have to feed in public; it covers a lot once baby is latched on; even my belly so no need for an undershirt.