This isn't BL, but it's about a girl who falls in love with a gay guy and starts to accept him for who he is. It adresses homophobia too.
Kare no Aijou no Hakari

Since it hasn't yet been suggested, I'd say go for Asterisk, it's mild. Really, really, really mild. It's so mild there's barely anything there. But it's cute, and there's a good bit of action, so if she likes Airbender, she'll probably like something like this. Try to start her out on anime, I've force-fed my friends Sekaiichi Hatsukoi down their throats, Kisa and Yukina episodes, and then the next thing I know, my friend tells me, 'I've never watched two guys kiss before, but now I've seen six kisses in one hour, this is all your fault!' and the next?

This one was about Viewfinder, 'I think they look good separately, but I think they look better together. Wait... What did I just say? See! It's all your fault! Now I'm thinking two guys look good together! Why am I thinking this way?' Oh, and my friends who can't take yaoi, absolutely adore Love Stage!!. So I'm going to second that suggestion. Izumi looks like a girl, so it doesn't offend their sensibilities so much, and Ryouma is way too adorable for words, they can't help but laugh at his antics.

Actually, it works best if you talk about it 24/7, just tell her the brief story line. Dear Myself and World's End works great if you tell them. I'm like a non-stop twenty-four hour BL live broadcast, my entire class knows about it, my entire family knows about it. And where they were once incredibly repulsed, they're now tolerant for the larger part, my closer friends and most of the girls are fairly interested; my mom, brother and the guys in my class joke about it good-naturedly. I quote, 'Hey, did you read fifty shades of gray?' A pause, and we all know what's coming. 'No, no, she reads fifty shades of gay.'

I'd recommend New York New York.

Due to my friend's love for BL and Yaoi, I have to face an everyday life at school being showered with numerous 'boy loves boy' stories. Eventually, I became accustomed to it. I read some she recommended and I found some that I personally like. Since I am a mild homophobe, I'd suggest :
Komatta Toki Ni wa Hoshi Ni Kike! - Sweet and humorous. The couple may not progress to lovers but any reader would see the deep connection between the two. It is a must read.
Seven Days - Really good for BL starters.
Kono Ore ga Omae Nanka Suki na Wakenai - Really sweet shounen ai manga. I really loved reading it. In fact, I have re-read it several times.
Aitsu no Daihonmei - I really loved this one! It's really sweet.
Hope these would help ^^