Like others, I was scared s***less the first time I went out dressed in public.
But basically, it reached the point where I couldn't hold it in anymore. I'd been dressing at home for a while, and was legitimately starting to see a girl in the mirror for the first time about 2 months into HRT, and it reached the point where my mind basically decided for me that it was time to go out. I obsessed over it, thought about doing it, and then every single night that passed without me doing it, it just drove me further and further up the wall, because I was obsessing over how I hadn't done it yet, and how I should.
So finally, that's what got me over the fear. I took video after video of myself to make sure I looked all right from all angles. Then after finally leaving the house I still sat in my car for over an hour, nearly talking myself out of it at least 3 or 4 times, before I finally realized, I was going to hate myself if I didn't do it. So I had to do it. Even if I didn't pass, I had to do it just so that I could quit with the self-hatred and self-criticism and obsession over it and feel proud of myself for being brave for a change.
It took months and months after that before I came even remotely close to being used to it. I only got the courage to go out maybe once a month. It got easier after I started going to a local trans support group and friends basically started forcing me to go out more. But even then, I never got used to "going out dressed." Over time, I slowly androgynized my wardrobe more and more, incorporated more and more feminine things into my everyday life, and then finally about 11 months into HRT the "ma'am"s started. And over time they got more and more consistent, until it wasn't even a matter of "going out dressed" anymore, it was just living life. And that's basically all I'm doing now. I'm not going out shopping in "girl mode" anymore, I'm just going shopping. That was when the nerves and the jitters basically completely stopped, when there ceased being a "guy mode" or a "girl mode" anymore, and I basically reached the point where I was a girl whether I wanted to be one or not.