I'm an American who married a (female) citizen of a South American country. She came into the states on a K1 fiancé visa, as Yung Havuk alluded to upstairs. (Btw, my wife knows about my ladyboy history).
The K1 fiancé visa process is daunting, time--consuming, and somewhat expensive with a myriad of little nickel and dime fees. Once approved, and after your fiancé enters the US, and after you marry within the mandated 90 days after arrival in the US, THEN the "green card" (permanent legal resident status) process begins. That'll take about 6 months after your marriage to obtain.
I did it all myself, sparing the cost of a lawyer. I have another friend who paid a lawyer to take care of everything. So, your time, temperament, and budget will determine how you proceed. Also, there are some online companies who specialize in facilitating K1 visas and green cards, and they seem to represent the "middle ground" between hiring a lawyer and doing it yourself. Thee are easily found by Google.
To obtain the K1 visa, you'll discover a lengthy vetting process which involves producing police reports from every place your lady has lived her entire adult life (if there is a history of prostitution on her record, you'll likely have a problem). She'll need to have a physical at a US government approved doctor in her hom country. There is an actual interview at the US embassy n her country. You'll need to produce a "history" that you and your lady are a real couple and not just a marriage of convenience to obtain a green card (you'll produce travel records, photos of the two of you...anything that can be considered "proof" of a relationship.
There are entire forums devoted to this subject and every aspect of the process. Worth checking out.
The hassle and expense are the bad news, but if you love your gal, then you'll stop at nothing. Go for it and do not be deterred to get started.
The good news. Your home state of California is same-sex marriage-friendly. To them, it should be just another, routine, K1 visa application.
If there are issues with her past (like prostitution or drug arrests), you'll have a problem, probably.
In that case, your K1 visa will likely be denied. I am told that IF you are already married though, then your case stands a better chance of getting approval for entry. (If already married, then the "K1 fiancé visa is a moot point, different rules apply for the already married).
One option, your budget permitting, is to travel to a country which is lenient about tourist visa requirements. Argentina comes to mind. There, they have an enormous trans-community, and same sex marriage is legal. You could legally marry there, let her travel to her home country, and then commence the process to get your Bona-Fide wife into the US. However, I don't know about how that actually works.....I just know guys who did it marrying Filipinos, Mexicans, Germans, and a South African.
Good luck!