She is interested in the conversation because she is intrigued by Darcy's complex character. He is reserved - he doesn't volunteer much information. But the Bingleys' are providing lots of personal tidbits. The whole dynamic of the conversation is irresistible to Lizzy, and the reader as well. It opens windows into all of their personalities. I can't say her interest in Darcy is impersonal, though. I rather believe she personally does not like him.