Of course there is nothing wrong with what you are doing and you should not feel ashamed in any way, and it really does depend on what sort of a person your girlfriend is. As you can see from some of the above posts, there are lots of ignorant people out there who just wouldn't understand, but at the same time there are many others who wouldn't have a problem with it.
If it's part of who you are, then you really should tell her if you ever want your relationship to move forward and to be truly happy. If she can't accept it then you will see eventually that she is not the girl for you and that you need someone who is more understanding.