The next morning Esther tells Jarndyce the rest of the story, which is, Oh, yeah, please don't tell anyone.
He's obviously fine with that, and everything is hunky dory.
Esther is worried about anyone else finding out, though. There's Tulkinghorn, who might know; Guppy, who she's pretty sure will stop poking around about her background, like she asked; and Hortense, who was so weird when she came to ask for a job.
Jarndyce says they can't really do anything about any of that, so not to worry.
He also says he has something to ask her, but he can't ask outright, so he'll write a letter.
She's all gratitude and feeling like she owes him big-time.
A week later she receives the letter. It's a...proposal of marriage! Yes, yes, we all saw that coming, obviously.
But still – isn't a tiny bit creepy, considering how she thinks of him as a dad, and how indebted she feels to him? It's a bit too much of a power imbalance to be OK.
The letter is nice and sweet and loving, and Jarndyce makes sure to say that no matter what her answer, it won't change how he feels about her.
Esther also reads between the lines to see that he's asking her now that she's no longer pretty, because she's unlikely to get another offer.
She starts to cry. Then she feels guilty for not being instantly happy about this and for still thinking about Woodcourt.
Finally Esther makes up her mind to say yes and burns the dried bouquet that Woodcourt gave her before he left for China.
A week goes by. Jarndyce doesn't say anything about the letter and acts totally normal.
Two weeks go by.
Esther comes to see him and says she has an answer. She hugs and kisses him. It's kind of an odd moment – instead of calling her his wife or his love or whatever, Jarndyce is psyched and calls her "the mistress of Bleak House," like she's marrying the house and not him (44.58). She doesn't tell Ada.