Ok, I imagine by reading your post that you are TV rather than TS.?
Although when first venturing out into the outside world, it is pretty much the same for both.
My advice would be to dress sensibly, just wear the same sort of clothing as you see women wearing every day of the week. Wear sensible make up, without going over the top.
Go to somewhere like a shopping centre where there are lots of people, and just mingle and mix in with them.
If someone does look at you a little strange then they probably have read you, or they may be unsure if you are male or female.
Just smile all the time., be confident and sure of yourself, and if someone looks at you, smile back.
If you do see someone who you know, don't panic, just carry on doing whatever you are doing, and don't draw attention to yourself. It is a 90%+ chance that they would not recognise you. Clothes and make up completely change someone's appearance. Where you would need to be careful is going in and out of your house, or getting in and out of your car. People easily recognise cars.
When I first started going out dressed, I was very young and naive. I still lived at home with my parents, so I would have to wait until late at night when they were in bed. Late nights and very early mornings can be dangerous if you are alone and not very confident and comfortable with yourself.
I had a very nasty experience that will live with me for the rest of my life. I was very lucky, as I got away. I could have been raped or even worse. But it was caused by my own inexperience and through being very naive.
I have been raped on 2 occasions since, but I was older then, and I knew what was coming.
When I first started going out I have seen many people who knew me, but I am sure that with one exception, none of them recognised me.
One woman who I knew even asked me if the last bus had gone. She either didn't recognise me, or if she did, she never told anyone.
The person who did recognise me was just as shocked at me discovering her secret, as I was with her discovering mine. We literally almost bumped right into each other.
She accepted me for who I was, and to this day, we remain best friends.
So my advice is, be careful, work out where you are going, pick somewhere with lots of people around, be confident and have your wits about you at all times. Don't go out alone very late at night, and above all smile at all times.
Hope this helps