Like many people, Dobbin is shy on his own behalf, but when he is trying to be altruistic, he has all the energy in the world.
While Amelia and George are on their honeymoon, Dobbin is in London trying to figure out the business side of their marriage.
He has dealt with the Sedleys, and now the time has come to tell the Osbornes what George has done. Dobbin decides it's better to first tell George's sisters about it, since girls are always romantic and won't be as angry as his father is going to be.
He hangs out with Jane Osborne, the older sister, at a party, and then asks to speak with her about something serious the next day. She kind of flips out a little because she is way into him and thinks he's about to propose.
The next day there is a pretty comical scene of misunderstanding. Dobbin is beating around the bush trying to get to his point, and she is beating around the bush trying to encourage him to ask her to marry him.
Finally he starts playing on her feelings about how romance and love are awesome, and also how men need to be honorable to the women who love them. When he puts it like this, she obviously can't disagree. So he tells her about George and Amelia's wedding, then he leaves.
Jane Osborne is bummed about the lack of a proposal but is OK with the other news. She tells Maria and Fred Bullock about it. Fred points out that George is an idiot who will most likely be disinherited. If that happens, then Maria and Jane will each get a lot more money when Mr. Osborne dies.