It's not just that Douglas talks in the frame narrative about how horrible the governess's story is—the frame narrative also foreshadows the horror to come in subtler ways, like when Douglas sets the scene by describing the ominous events preceding the governess's employment at Bly:
There had been for the two children at first a young lady whom they had had the misfortune to lose. She had done for them quite beautifully—she was a most respectable person—till her death, the great awkwardness of which had, precisely, left no alternative but the school for little Miles.
The fact that the previous governess died under ambiguous (or, at the very least, unrevealed) circumstances doesn't bode well for the incoming governess. In fact, the unnamed first narrator (who's listening to Douglas's preface of the story) points this out:
"In her successor’s place," I suggested, "I should have wished to learn if the office brought with it—"
"Necessary danger to life?" Douglas completed my thought. "She did wish to learn, and she did learn. You shall hear tomorrow what she learned. Meanwhile of course the prospect struck her as slightly grim. […]"
The job that the governess has before her is, indeed, "grim," and readers certainly feel this ominous quality as they anticipate the impending story. It's also quite ominous that other women refused the role of governess because of the employer's request that they never contact him about any matters concerning the children, regardless of what happens. All of these details foreshadow the terrible time the governess will have at Bly, though the governess herself ignores the warning signs. At the same time, though, it's possible to argue that these warning signs are precisely what predispose the governess to jump so quickly to thoughts about ghosts and apparitions in the first place (this argument would align with the interpretation that the governess is unstable and that the ghosts are her own invention).
Many of the interactions that the governess has with Mrs. Grose contain some foreshadowing, as the governess senses that Mrs. Grose knows more than she’s letting on. For instance, when the governess first meets Mrs. Grose in Chapter 1, she's a little disconcerted by just how glad the older woman seems about her arrival:
The only thing indeed that in this early outlook might have made me shrink again was the clear circumstance of her being so glad to see me. I perceived within half an hour that she was so glad—stout, simple, plain, clean, wholesome woman—as to be positively on her guard against showing it too much. I wondered even then a little why she should wish not to show it, and that, with reflection, with suspicion, might of course have made me uneasy.
What's especially ominous about Mrs. Grose's excitement is that it suggests that she's desperate to have a competent and capable adult at her side, implying that there's something ominous about Bly—something Mrs. Grose seemingly needs an ally to face. And yet, the fact that she doesn't want to show her excitement makes the matter all the more sinister, as if Mrs. Grose knows something so frightening about Bly that she feels she must keep it a secret for fear of scaring the governess away.
The sense that Mrs. Grose knows more than she's letting on intensifies in Chapter 5, when the governess tells Mrs. Grose about seeing the figure on the tower and outside the window. Reading into the older woman's reaction, the governess senses that the information has awakened something in her. The governess recognizes a "glimmer of a consciousness" in Mrs. Grose that she hasn't seen before, and it seems as if the news of the strange sightings has given Mrs. Grose an idea that is still "quite obscure" to the governess herself. In other words, she can tell that Mrs. Grose is thinking about something important but not fully revealing her thoughts.
Much later, the governess finally insists on learning the whole truth, demanding that Mrs. Grose "give [her] the whole thing." But this doesn't happen until the end of Chapter 7—and even then, Mrs. Grose only hints that Peter Quint and Miss Jessel (the ghosts the governess has supposedly been seeing) had some sort of relationship and that Peter Quint "did what he wished" with Miss Jessel and (it's implied) the children. Even when Mrs. Grose supposedly tells the governess "the whole thing," then, she doesn't end up saying much. And this sense of withholding adds to the tension throughout the novel, hinting that something sinister has taken place at Bly and that the governess will eventually have to face what has happened. What's most disconcerting, though, is that she never truly comes to understand the nature of what happens at Bly. In a way, then, the novella's use of foreshadowing never fully reaches a conclusion—it just hints at a whole world of loosely defined terror, thus contributing to the narrative's unsettling ambiguity.