I'd bring up the North Carolina bill.
http://www.thegailygrind.com/2016/03/24/trans-man-destroys-north-carolinas-dangerous-new-anti-lgbt-law-in-one-brilliant-tweet/If she's like "oh gross a trans guy" then... actually, I wouldn't call it quits quite yet. Where most people are aware that transwomen exist, I feel like transmen are relatively unknown. If you bring this to her attention, it may well be the very first time she's hearing about transgender issues outside of Caitlyn Jenner.
If you're ready for some ignorance, you can prepare for the conversation. Have some talking points ready; for instance things about compassion and trying to see things from others' perspectives, about accepting people who don't fit the norm and taking their experiences seriously. Perhaps mention that you have transgender friends, and that this is important to "some of the most important people in your life." (that's my favorite phrase, but I'll let you borrow it
)
It's important not to lie. It's really hard to back down from a lie. Talking about friends and referring to yourself obliquely will make sense to her in the future, and will lessen the perceived violation of trust. So if she asks if you're trans... be willing to cop to it, but you don't need to come out immediately. You might hedge a little... "I know it's hard for transgender people to date... how would you respond if I was?" If she says that she'd freak out... try to build a conceptual path to acceptance. She'll be freaked out by that, but the uncertainty will keep the door open just a little longer.
It's seen as somewhat irregular for guys to be accepting, much less supporting, of women's rights, gay rights and trans* rights. My expectation would be for her to be suspicious after that kind of conversation. Mention it, have a little conversation, and drop it. After a little wait, talk about transgender issues again. Depending on how things go in that second conversation, either ghost her or use it to segue into outing yourself.
