When I am out with my husband, he is super helpful and will hold a blanket over me and baby until I can get situated. I am a bit "busty" and just not that graceful sometimes! Once I have baby latched correctly, he just situates the blanket around us and sits down. No big deal. Also, if we have a conversation during this, then no one seems to notice or stare. Whatever.
We have done this for our first two, mostly for his comfort level. When he isn't there, I just sit down and work it out as quickly as possible. I can't help it if someone thinks it's rude that my baby is hungry! I am nobody's sex object except for my dh!
For coverage, I bought a belly band, which is great because, although I prefer not to show my belly, in the winter, the draft is a killer!
Once you do it a few times, you can usually work out what makes you feel comfortable, and it stops being such a big deal. Feed the baby and move on. It shouldn't be such a big deal, but some people can't mind their own business and are critical. Just ignore them!