The Bell Jar closes just as Esther enters her exit interview at the psychiatric institution where she has spent the past few months recovering. Since the novel stops there, we can't know for sure what happened in the interview, whether the doctors decided that Esther was ready to go back to college, or whether they decided that she needed more therapy.
But we do know that the novel is being narrated at some point in the future by Esther. Let's just call her "Future Esther" for convenience. The only hint that we get about Future Esther's life is that for a "long time afterward," she couldn't bear to look at the free stuff she got at her summer internship, but when she was "all right again" she brought the stuff back out, used the free lipstick still (not sure how long lipsticks lasted in the 1950s), and "last week" gave one of the freebies to her baby to play with (1.13). Future Esther has managed to have a child and write this narrative, two things that weren't supposed to be possible together, according to many of the other characters in the novel.
But it isn't clear under what conditions she was able to do both, to have her cake and eat it too, if you will. It's not clear whether she's married, whether she was finally able to find true love, or whether she had the child out of wedlock. And it's certainly not clear whether she will sink into a suicidal depression again. In some ways, this early passage is the real ending to the novel, although it leaves just as many questions unanswered.
Of course, the temptation is to read Plath's life back into the novel. But just because Plath ended her own life does not mean that Esther Greenwood, a fictional creation, also committed suicide or was intended to commit suicide by the author. That would be missing the whole point of writing fiction, made-up stories.