Hi Bethany W
Short answer you do not bring it up and yes it would be extremely rude to out her.
Long answer. It does not matter whether she is or she is not and you must accept that she is a female first and foremost and treat her as such. If you wish to reveal that you are a cross dresser or that you are considering transition then do so on the assumption that you are revealing your personal life with no expectations that your friend will reveal anything personal about her life and as you have said she is a new friend. So I would assume that trust has not developed that deeply at the moment, between both of you.
If you decide to tell her about yourself, then as Jacquelyn said, tell her what you have done, what you are considering doing and your gender issues. Your new friend will either help you or not and maybe tell you something personal about herself. Her reactions are unknown at this stage as you have not really known her for that long.
Why? Because from my perspective or personal views. It is my decision and my decision alone whether I tell anybody about my past. Regardless whether they know, think they know or they don't know, it does not matter and if they are an understanding, compassionate person and a real friend they would not say anything anyway and if they said anything then they would not be a friend of mine.
I hope things turn out well for you and your new friend.
Kind regards
Sarah B