It's up to you, but I doubt I'd find it embarrassing. I've been getting mammograms for sometime now - not only do you have to go topless in front of the tech, she gets to haul your breasts around into strange and unnatural positions to be squished.
Good point. At least the bra fitter isn't going to twist your breasts around and mash them into pancake-flat proportions. Or, if she does, you know that's a bra that REALLY doesn't fit.
For a bra-fitting-lite, go to Victoria's Secret. They just fling a tape measurer around you a couple of times fully clothed, and give you a size, which is based on the ratio between your bust at the widest point and around your ribcage. Then they give you a bin full of bras in that size to try on. You go into the dressing room, try on the styles you like, figure out which fits best, then go out and buy however many in that style in whatever colors. I find it really convenient, and their bras are pretty good. And of course once you know your size and style you can buy replacements online.
It's SO much better than buying bras in a department store, where you have to keep going back with all kinds of different brands and sizes and styles, most of which don't fit -- and then when you're done, fit the straps back into those teeny little hangers.