I never thought of putting a stretchy vest top on underneath (might try it though!) I usually just try and sit in a solid-backed chair or with my back to a wall so no-one's behind me to see my exposed muffin top.
Going back a few years, I think I can pinpoint the moment it got easier for me: DS1 he was particularly fussy one day, and chose his moment to arch backwards off the boob when the waiter had just brought the food. Waiter naturally looked to where the movement was. Waiter saw my nipple.
THE WORLD DIDN'T END! 
He looked away when he realised what he was looking at, DS1 was coaxed back onto the boob, and the waiter asked if he could get me anything else - no smirk, no blushes, just matter-of-fact. After that, I stopped worrying so much.
I'd echo what others have said - it's people you know who have the oddest reactions! DP's friends clear the room when they realise I'm about to feed DS, and I'm left on a huge sofa on my own whilst they huddle out in the conservatory. I tell myself it's because they all secretly fancy me. 
(And none of their wives/partners ever breastfed so they aren't used to it...)
I met up with my work colleagues for lunch, and most of them didn't bat an eyelid, except one who awkwardly made a joke and didn't know where to look, shifting in his seat. He'd never had kids though.
I think other people's reactions say more about them than you. Be brazen and confident, just do it, and it will be as easy as you want to make it.