Be careful what you wish for. You just might get it.
Marianne has been expecting, wishing and hoping to see Willoughby, but he doesn't turn up to pay a call, despite a number of days passing by. Marianne is quite obviously in the doldrums, and is starting to let herself go - she pays little attention to her hair and clothing, despite the fact that she's going to a party with Lady Middleton. It figures, does it not, that she'd bump into Willoughby now that she's not really looking all that well?
Infuriating Willoughby, who is deep in conversation with a fine young lady. He pays the minimum attention required to the Dashwood sisters, only to have Marianne make a bit of a spectacle of herself by speaking in familiar terms (she calls him "Willoughby", not "Mr. Willoughby", which is a huge distinction at that time - at least she didn't call him by his first name, I suppose), and by holding her hand out for him to take, rather than simply curtseying as she ought to do. And then, in the presence of other company, she asks whether he's received her letters. Good Lord, Marianne, at least TRY to show a bit of restraint. *headsmack*
And Willoughby . . . well, he's obviously embarrassed. And avoiding her - he tries to avoid seeing her (even though he's seen that she's there), and he doesn't meet her eyes. Rather than allowing her to stand there with her hand out, he does take her hand, but only for a second, and he barely touches her. His words are stilted and proper and, well, pretty scanty, really. He makes no explanations, asks nothing personal, and doesn't even say that he's happy to see them . . . nor does he appear pleased. He tries to downplay Marianne's correspondence to him, acting as if she's just sent him a bit of business correspondence, so it can be inferred that he's trying to downplay their relationship, and possibly also to convey the impression that she shouldn't have been writing to him.
Mrs Jennings is not at the party with them because she is off with Charlotte, who is giving birth. This is not an inference - it's actually plainly stated (for the time) by mention of Charlotte Palmer's "indisposition".
And in the book, Elinor and Marianne interrupt Lady Middleton in order to get a ride home, since Marianne is so overpowered by emotion (and the heat of the assembly). But I much prefer the version of this scene as it plays out in the 2008 BBC/PBS miniseries, since Colonel Brandon turns up in ActionRescue! and HarshGlare! mode: