Ignore them staring eyes, just walk with an air of confidence as if you are completely normal and they are the ones with problems, after all, the reality is they do have problems, if they can take enough time out of their lives to give you such wonderful attention. I know its difficult, but I had to deal with that for a good year+ before I even got on hormones and was dressed completely as a woman (nothing outlandish, but still feminine enough to put a target on me), and did not quite fit the look well then. Show no fear, don't give them any attention, after a while you won't even realize they are even paying any attention to you, so long as they keep their distance (gawking and whispering) and don't confront you, no harm done, this you can deal with.
Oh, and I wasn't confident right away with trying out women's clothes either, not in public, at first I'd find things in catalogs and pick things out, but it was always difficult knowing if things would fit properly. Eventually I did have the courage to buy clothes in stores, but it was especially difficult for me to look at bras in panties in stores, always got nervous so bad that I'd sometimes get dizzy, because I knew I was being watched, that I didn't quite fit the part, but it got easier as time went on, those hormones did wonderful things with my face, body as well as my whole demeanor. Now, because I do fit in completely, I have no problems at all with whatever I'm shopping for, no more fears. You'll get there, just give it time, build up your courage a little bit at a time.