In my first year of photography school I was hired to photograph a master class given by Leon Fleischer, the famous pianist. Also being a musician, this was a jaw-dropping opportunity. Being so green, I lacked the boldness needed to get the shots, so hunkered-down in my front-row seat with a telephoto I shot just under two rolls of 35mm. My employers were not happy, and I still kick myself for the blown opportunity.
I finally overcame my shyness after my first season shooting weddings. I no longer do them, but because of that it doesn't bother my to candidly shoot people, even if they see me doing it.
I do a moderate amount of street photography, and for me it's two things: a) Practice doing it in a comfortable way for a few weeks or months, until one day you're in a rotten mood and don't care, or are otherwise feeling extraordinarily confident, and that will set a future tone; and b) As RML and others have said, if you're just doing what you're doing, most won't notice and those that do, won't care.
Rob