"That would be me." After a moment of hesitation (but just a moment), she offered her hand to him.
You'd think that after a few thousand years of socializing with mortals, she'd get the hang of it. Apparently not as much. Then again, when muses fraternized with mortals things tended to go awry rather than well.
"It's a pleasure to meet you in person." Because knowing things about someone was always a little odd until you fully put a face to the knowledge.