If you really have an urge to go outside but you can't show yourself around your home. Why don't you go to a nearby town or something? This way your girlfriend couldn't complain about it either simply because you are doing it somewhere else in a place where no one knows you.
The harder way is to have a nice long chat with your girlfriend about this matter. It would be much harder but the reward might be much better but on the other hand there is always the possibility to for it to turn worst. However, if you are in a relationship you should talk about it with your partner. Simply express out your feelings as good as you can about this matter. I'm sure that most partners will be able to understand and some might even turn supportive.
Myself, I once wrote a letter to my wife because I didn't know how to express all this in one go and I tend to express my feelings much better in written form than in spoken. I sat down and wrote the letter for two hours at the middle of the night(it's the time when I got the urge to write the letter and explain everything). Since she read the letter she's much more understanding about me turning into a girl. You will have it much easier because you won't be turning into a girl but you still want to stay male.
