Which country/state are you in? Someone here will probably have some experience in getting HRT in your area.
Keep communications with your girlfriend open, but don't push the trans issue too much. She's going to need time, there's going to be the worry that you're going to become a completely different person once you're on hormones, but with a bit of luck you'll work things out. Good luck making the first steps to transitioning and hopefully someone will be able to help more.