Hi I'm from the UK. I go out a heck of a lot these days and I really don't have any issues really. It's all about confidence and when you are out and about to just act as if it's 100% normal and you will be perceived as a normal woman going about her business. The one thing that gets us made the most is body language I have found as nervousness attracts attention. This is all easy to say, but at the start of me going out I was a bag of nerves!! it gets easier eventually, just takes time.
I started out by going out driving which is a safe environment and then walking around places like the Cemetery which is quiet and then moved onto a walk around the park. Now I go shopping a lot to supermarkets & clothes stores and I was even out with the girls last friday night!
Just think about where you are going and think, would a GG go there? try to avoid teens and groups of men with thier mates as they will out you if you give yourself away. Always dress appropriately for the situation too. Look at what real women are wearing and copy them.
You could always try a Cd/Trans friendly night out or event. I'm not sure where you are, but have you heard of Leeds First Friday? have a look online, I go there with the girls and its very accepting and a fun place to go out and I spoke to a lot of girls out for their first time.
Hope this helps.
