Perhaps I missed something in this conversation. Is that something you would want to use "background" to rules-model? I would think that it would be something that you would just declare your character to be, and pick something else as a background.
But if I try to answer your question: Stat Bonusses, when it comes to background, tend to be based around the sorts of things that a background would teach. The kind of vigorous "exercise" that you would have gone through during your time coming up as that background. Being cis, I wouldn't presume to know what that would entail for a "trans-woman" background (and again, I'm not sure that I'd use "background" to model the trans experience in a game - it seems like an odd fit to me).
But if you don't mind a somewhat tongue-in-cheek answer to your direct question, I'd say: CON (for your handling of the 'slings and arrows'), WIS (for figuring out who you are), and CHA (for the confidence and strength of character that comes, and was needed, to transition.)
Note: If any of the above is wrong, please forgive me. I'd like to consider myself an Ally, but I admit that I have much to learn.