Personally, I'd try the letter idea. A postcard might be a little off-key - you've said you're close to her, and unless she likes the short-and-to-the-point, maybe she might be offended that you didn't tell her why.
I've been thinking about the postcard idea myself, actually, to send to my parents - I'm dedicated on telling them this summer (due to practical reasons), and I feel like a nice handwritten letter explaining it all would be the best way. My sister is the one who I feel more like I should tell, and I'm pretty close with her, unlike my parents. It feels wrong to be keeping her in the dark, and I feel like she might take it the best out of my family, seeing how she has many LGBT friends and her best friend is gay. My parents, on the other hand, I could care less about how they will react (badly) - it's up to them to come to the table and accept me, not the other way around.