I think I can give a reason Darcy asked Lizzy for a dance and then left; he saw she was flustered and played the gentleman by giving her a chance to compose herself.

...[Lizzy] was in conversation with [Charlotte], when she found herself suddenly addressed by Mr. Darcy, who took her so much by surprise in his application for her hand, that, without knowing what she did, she accepted him. He walked away again immediately, and she was left to fret over her own want of presence of mind.... (Ch. 18)

Darcy first approached Lizzy at the Netherfield ball almost as soon as she arrived. Whether Darcy just hung about Bingley as he greeted his guests or made it a special point to greet Lizzy as soon as he saw her, I cannot say. Nonetheless, Lizzy (having just learned of Wickham's absence) responded to Darcy with barely restrained anger. So when Darcy asked her to dance and found her somewhat flustered, he could easily have thought that retreat was wise both out of consideration for Lizzy and to remove himself as a target in case she was still angry at something.

We disagree whether Darcy wanted to talk to Lizzy during the dance, but I have said what I had to say about that elsewhere in this thread and need not repeat.

I wonder if Darcy's lurking near Lizzy and Collins after the dinner break was to try to figure out why Collins was constantly hovering about her. I have no idea whether Darcy saw Lizzy's humiliating dance with Collins. In some adaptations it appears one of the reasons he asks her to dance himself--out of compassion--but the text nowhere suggests that. Still, Darcy, seeing Lizzy and Collins together could wonder what the attraction was and if it was mutual; I dare say a man can be bothered by a lady's attraction to someone else without ever intending to marry her himself. (Both the early Brandon and eventual Willoughby come to mind in S&S, or conversely Emma's jealousy of the idea that Knightly might marry Jane Fairfax.) He could not ask her to dance after dinner (even if he wanted to, which I doubt) since Collins was making it impossible.

I think already at the ball, Darcy wants Lizzy to like him--or at least respect him. He might say his pride would demand it, although I suspect there is already more to it than that, deny it as he will. I think her preference for Wickham in spite of his assurances (during the dance) mystify him; thus his blame for Wickham.

...[Darcy and Lizzy] went down the other dance and parted in silence; on each side dissatisfied, though not to an equal degree, for in Darcy's breast there was a tolerable powerful feeling towards her, which soon procured her pardon, and directed all his anger against another. (Ch. 18)