Here's my question:

If your girlfriend and mom have no idea you are wearing, what on earth are you so worried about? They are probably the two people who see you the most. If a girlfriend can't tell you are wearing a hair piece, then you have nothing to worry about.

I would tell her though, maybe in another month or two. You don't want to tell her right away, but you don't want to wait until a proposal either. If she doesn't notice anything in a couple months, telling her should be easy enough and should not change a thing because, well, she never noticed in the first place.