The fact that you "really want to do this right" will go a long way to help make your road to acceptance a smoother one. Patience and honest communication are absolutely crucial now because a certain amount of lost trust will have to be regained due to the fact that you hid your cding for a long time.
But it sounds as though you're adeptly helping her through this time of overwhelming confusion as she tries to wrap her brain around this whole thing. After all, you've had most of your life to adjust to this part of your personaliy, she's had a month. And she seems to be doing it with lovingness and grace.