Well, Alan, in the presence of any attractive woman, any man (AS or NT) will flutter nervously. First, you probably shouldn't introduce yourself as originating from the Fourth Bountiful Human Empire irregardless of your Dr. Who-like charms .
Seriously though, the best way is to let her know you're there. But instead of being direct, try to be more subtle. Keep your cool. Don't stare at her awkwardly (only when she's trying to communicate with you. Even then, don't stare at her too much). If you're going to ask her questions; ask her after you've said hello. But, asking too many questions will make you seem creepy because it'll sound more like an interrogation rather than a genuine conversation.
But for me, I find compliments work best. Women love compliments. Compliment their shoes and they'll go on and on about their shoes. Likewise, what is it that you like about her?
Obviously, she's attractive. But beyond that, what do you enjoy about her behavior or demeanor? Do you find her comments on a particular subject interesting? If so, compliment her on that. It'll open up a window for conversation.