The more you do it the less you care. Or at least you realise that even if the baby is mucking around people genuinely don't notice. They really don't. I know it is purely anecdotal but 3 children, all bf and I have never had anyone stare, the odd misty eyed old lady telling me how lovely it is but no daggers. If you have a baby that bobs on and off a lot tuck a muslin into our bra as you feed and keep one hand under the baby on the edge of your bra so when you feel him come off you slip the muslin up over your boob as he comes away and hey presto, all covered up.
My BIL once walked in on me bf my dd. like you I was feeling shy so had carted myself and dd off to the bedroom at grandparents house. BIL forgot we had swapped the room we usually sleep in and as I was in a bedroom I let it all hang out.it took him a few seconds to realise what he was staring at, then he blushed bright red, mumbled an apology and fled. He's much younger than me so was mortified. I still tease him occasionally but now on my second, I use my trusty shawl, stick my chin out and pretend I do this all the time and am not in the least bit shy about it. Deep down it isn't so