Heather, just jump in, the water is fine! I spend way too long, almost 50 years, waiting for "just the right time" but when I finally got going "out the door", there has been little stopping me and I can honestly say NO BAD REACTIONS.
If you're worried, that will show to some extent, which will only set off people's radar, but if you believe you are just a woman out for a day of shopping or whatever, you will draw little to no reaction if you are dressed close to the "norm".
Way back in the day I went out to the local mall in a hot pink wrap dress, white stockings and 4" pumps, the best thing I can remember is that it was almost empty. My last outing was about 4 hours, 2 of which was shopping with a CD/TG friend, an hour at Panera and finally an hour in a convenience store, super market and a few clothing stores. Other than one "second glance" at a high end store, no one really even appeared to notice me and at almost 6'/260, someone should have. I was dressed in a casual manner, black/white/green pant set/cardigan, very "blendy" so very successful. Just put on a low key outfit and go give it a try, you'll only regret not having done it long ago!