When I'm shy and consequently awkward guys typically think that my being shy, nervous and awkward is "cute". The guys I've dated were always warned by me about my SA, and they didn't seem to mind at all in a negative way. You know how those loud, dramatic girls are SOOO annoying?... I think quiet people give off the "I'm not all about drama" vibe (and it's typically true)
I have really high standards when it comes to what I consider love, and everyone is different about that... but I've truly been in love once, with my ex-fiance, and at that point I was completely "me". He made me feel comfortable, and around him I think my SA actually went away completely (well when it was just the two of us at least). I could tell him anything... he was my best friend that I'd ever had (crap, now I'm getting sad... ) When I was with him and others, I was socially anxious, but he understood and knew how to make me feel more comfortable. Once when we went bowling with his friends I started getting really bad anxiety and even though he paid for the full length of bowling, he told his friends that HE wasn't feeling well and he took me home where we just relaxed in comfort and he just made me feel much better. He knew that telling his friends what was really going on would just make me more anxious, so he said he wasn't feeling well. Though I was with him for years and he did many amazing things along those lines, that memory always stands out - I guess because it's just how he casually cared about me and took the time to understand.
Sorry, I tend to ramble about him. He still breaks my heart. You'd think by now it would just be shattered and unable to crack any more than it already has... but it was love, and love makes you crazy. I was ready to spend my life with him.. Uh, until he beat me..
If you're truly in love, she'll understand or she'll at least try her hardest and do what she can to make you more comfortable. If the girl in your avatar photo is you, well, I'd go lesbian for you (kidding, but you're gorgeous!), you seem quite sweet, and I absolutely doubt that your girlfriend is bothered by your anxiety. She wouldn't be with you (and she definitely wouldn't love you) if she was really upset about how you act because of your SA. I imagine that she thinks it's cute, and she likely understands.