How do I get the courage to sing to my girlfriend?

I'm an amazing singer. I'm in a band as the lead singer. I and my girlfriend has been together happily for a long time and she recently discovered I'm in a small band. (It's kind of a pathetic band, really. So I've never mentioned it.) Ever since she's heard she's always wanted me to sing to her. And today I was prepared to sing our song to her romantically under the stars. I slipped my plan and so she was dying to get outside so she could hear me sing to her. I guess I was ready, and knew I could do it. I knew the song really well and all. But I could never do it. I had to leave with her sad and dissapointed. It makes me feel horrible. I mean, I'm an amazing singer honestly, and I love her so much. But whenever I'm about to, my heart starts pounding, I get really shy, and mix the words up in my head and nothing comes out. I sing around the guys in my band, and the audience we usually have, but with her it's so different. I promised I would sing to her very soon. I really need advise to get over this and just let out what I know I have in me. Please somebody help me before I blow it again. I've never sang to anyone I truly love before. I don't want her thiking I don't like her or that I can't sing. Please help.