That is a wonderful question, because it touches on the central idea of the play: Does society mold you, or do you mold yourself?
In the case of Eliza, we should take into consideration that she already had an inkling that she wanted a change for herself. Like she says in Act 2,
THE FLOWER GIRL:I want to be a lady in a flower shop stead of selling at the corner of Tottenham Court Road. But they won't take me unless I can talk more genteel. He said he could teach me. Well, here I am ready to pay him—not asking any favor—and he treats me as if I was dirt.This being said, we can safely assume that Eliza already wanted to be someone different; the "call" was already within her. The idea about the bet was the creation of Higgins, alone to boost his own ego. Therefore, Eliza's change in mannerism and speech is mostly the icing on the cake; she already felt the need to become a better person. Yet, not all is as rosy as she pictures it, because when she learns to speak properly she realizes that she no longer belongs in the world of the "old" Eliza. Now that she has seen what it is like to be treated like a lady, something inside of her is basically telling her that she has reached a pinnacle; it would be quite wrong to go backwards now. Therefore, it is not the language that changes her, for Eliza continues to have the same feisty personality. It is the fact that the language opened the door to her to a new world where she felt that she was, for once, no longer at the bottom of the "food chain". Hence, the only thing that Eliza can do now is to move on, and continue with a life worthy of a lady, no matter how mysterious that world may be. This is why in the end, when she marries, she does it more out of social expectation than love. Like Eliza explains, herself, in Act III
LIZA: [...] It was just like learning to dance in the fashionable way: there was nothing more than that in it. But do you know what began my real education?PICKERING: What?LIZA: [stopping her work for a moment] Your calling me Miss Doolittle that day when I first came to Wimpole Street. That was the beginning of self-respect for me. [She resumes her stitching]. And there were a hundred little things you never noticed, because they came naturally to you. Things about standing up and taking off your hat and opening doors—However, in the end, we know that a few other calamities do await Eliza. Although, all of them are part of the person that she will eventually become.
That is all. That is how it has turned out. It is astonishing how much Eliza still manages to meddle in the housekeeping at Wimpole Street in spite of the shop and her own family. And it is notable that though she never nags her husband, and frankly loves the Colonel as if she were his favorite daughter, she has never got out of the habit of nagging Higgins that was established on the fatal night when she won his bet for him. She snaps his head off on the faintest provocation, or on none.So, as you can see, Eliza continues life as usual at the end, still arguing with Higgins, still appreciating Pickering, and handling the jobs of the flower shop, as well as her home. The language does not change Eliza. It is the kindness of someone like Pickering which helped her feel worthy of being accepted and loved for who she is.