I found that for the first few months most of my maternity shirts worked well (mostly t-shirts). The extra material covered me and fit around me. When my tummy got small enough, then normal shirts worked pretty well. With my first I was much more worried about being covered than I was with my second. (For the first month or two or three- it is really helpful to be able to see the baby - as they need the help to get to the right position.)
I tried using a blanket over me, but that usually was a royal pain.
Nursing in your car is really private - someone would REALLY have to be looking to see anything.
Are you worried about your comfort, or not offending people around you? (Only my mom has commented when I was nursing in public (at a wedding reception), she thought it was something to be more hidden. (The other people at the reception did not comment at all.))
Mostly I have found that the right attitude goes a long way. :) The attitude is "My baby is hungry, I am going to feed him/her - don't look if it bothers you."
That said - I do try to find a quiet corner, or somewhere slightly out of the way to nurse. (On a shelf in between items at Costco (it was comfortable, and the right height!), next to clothing racks at stores with clothing racks, in my car....) I don't go to public bathrooms, and I have not gone to fitting rooms - as bathrooms are gross, and fitting rooms are boring. (More fun for mom to look around while little one is nursing.)
Anyway. You asked a simple question, and here you got a epic in response. :) Hopefully something of this is helpful. :)