Female pop geniuses who exercise their gifts in rampant, restless fashion over decades, writing, performing, and producing their own work, are as rare as black opals. Shape-shifting brilliance and an airy indifference to what’s expected of you are not the music industry’s favorite assets in any performer, but they are probably easier to accept in a man than in a woman. And such a musician, even today, is subject to the same pressures that have always hindered women’s artistic expression. Like the thwarted writers whom Virginia Woolf described in “A Room of One’s Own,” the female pop original is “strained and her vitality lowered by the need of opposing this, of disproving that”—by the refusal to please and accommodate that only a deep belief in one’s own gift can counteract. “What genius, what integrity it must have required in the face of all that criticism, in the midst of that purely patriarchal society,” Woolf writes, “to hold fast to the thing as they saw it without shrinking.”

Kate Bush, the English singer-songwriter, is one of those who have held fast without shrinking, so it is curious and instructive to see how certain cultural signifiers have been trotted out over the years to diminish her. Certainly, she’s had her share of respect and even adoration. Prince, Peter Gabriel, and Elton John collaborated on songs with her, and she has inspired younger talents; Tori Amos, Björk, Joanna Newsom, St. Vincent, Perfume Genius, and Mitski are all heirs. Every year, around the world, people get together by the hundreds to dance in public to Bush’s “Wuthering Heights”—a goofy but heartfelt tribute to her interpretive dance moves in the song’s glorious freak flag of a video. She’s got credit for her pioneering use of the Fairlight synthesizer, in the eighties, and the headset microphone onstage, for producing her own albums, and for evolving an ahead-of-its-time sound that combined heavy bass with the ethereal high notes, swoops, and screeches of her own remarkable voice. She is a dark-haired, dark-eyed beauty, and critics have always noticed that.

And yet—in part because she emerged into the public eye at just eighteen, and with “Wuthering Heights,” surely the most literary and therefore one of the strangest hit singles in history—Bush struck some people as a wide-eyed sprite to whom music somehow happened, not an artist fully in command of her own ideas and craft. The evidence against this reading, even then, included the fact that Bush had defied EMI record executives to pick “Wuthering Heights” as the lead single from her 1978 début album, “The Kick Inside”; it went to No. 1, making Bush the first female performer with a self-written No. 1 hit in the U.K.

In “Under the Ivy,” the music journalist Graeme Thomson’s smart and respectful biography of Bush, from 2010, the author describes how, early on, reactions to Bush often condescended to her as a child of privilege. She was a doctor’s daughter from Kent, raised by an affectionate, mildly oddball family in a rambling old farmhouse (I kept thinking of the Weasleys from the Harry Potter series), where she was kindly listened to and afforded time and space in which to play the piano and write songs. It was a house full of hidden corners and secret-garden nooks, a portal to the imagination almost as good as a magic wardrobe. The family was Catholic, and Kate, the youngest of three, attended convent school; home, meanwhile, was vibrant with the Celtic singing and sayings of her Irish mother. The twin influences of mystical Irishness and Roman Catholicism bequeathed an atticful of imagery to Bush’s songwriting. Her two older brothers, John Carder and Paddy, were early creative collaborators who became lifelong ones, introducing her to prog rock and the pre-Raphaelites, and, in Paddy’s case, playing a startling array of instruments. Her mum and dad loved her songs, even the ripe ones about adolescent sexual longing. “Our father bought a good reel-to-reel tape recorder,” John Carder writes in his book “Kate,” “and we assiduously recorded all her songs, typed out the lyrics, catalogued them and then posted the tapes to ourselves in registered envelopes—the simplest way of preserving copyright.” Later, a college friend of John Carder’s got David Gilmour, the guitarist for Pink Floyd, to come listen to young Kate play at home, and Gilmour, impressed, arranged recording sessions for her at a London studio.

Thomson contends that, at a time when musical camps were more fiercely armored than they are now (remember when people had to choose, absurdly, between punk and disco?), Bush got a bad rap from some music journalists for being a dreamy middle-class girl rather than an angry working-class bloke. There was grumbling about her tweeness, her witchy, unapologetic femininity. “Most of her records,” the jazz critic Richard Cook, writing about Bush in Sounds magazine, complained, “smell of tarot cards, kitchen curtains and lavender pillows.” That said, John Lydon—a.k.a. Johnny Rotten—loved her music. In a BBC documentary about Bush, from 2014, he allows that “a lot of my friends at the time couldn’t bear” Bush’s high-pitched, passionate warbling on “Wuthering Heights” and other early songs. “They just thought it was too much”—and, indeed, Bush is the high priestess of too much. “But that,” Lydon said, “was really what drew me in.”

In the nineties, when Bush’s output slowed and her public appearances dwindled, the British tabloids seized on another archetype for her: she was a “mythical recluse,” as Thomas writes, a rock-and-roll Miss Havisham. It’s a persistently alluring reversal-of-fortune story—the celebrity, especially one who blazed early and prodigiously, fading away, vain and lonely, ideally in a mansion. (See narratives stretching from “Sunset Boulevard” to the 2017 podcast “Looking for Richard Simmons.”)

But her real story doesn’t conform all that well to the fable. She was most productive between 1978 and 1994, when she made seven albums, but in the years since, she’s put out two critically acclaimed albums of original material plus a live album and a collection of some new versions of her old songs. She’s raised a son, Albert, who’s now in his late teens, with her partner, the musician Danny McIntosh. In 2014, she put on “Before the Dawn,” a twenty-two-night residency at the Hammersmith Apollo, in London, that combined theatre, puppetry, film, and music in a spectacle that critics found occasionally ridiculous and genuinely, almost unbearably moving. Tickets for all twenty-two performances sold out within fifteen minutes online.

In late November, Rhino Records put out a boxed set of Bush’s albums, plus some previously unreleased covers, B-sides, and other rarities. So, I spent most of a week last month in a Kate Bush-induced reverie—or was it a swoon? I know there were tears: you try remaining dry-eyed listening to “This Woman’s Work” on a cold November night after a glass or two of wine; if you do, I don’t want to know you. There may have been some ecstatic dancing that alarmed the dog; there was definitely some animated texting of lyrics to my children, who, at twenty-two and nineteen, are both, bless them, Kate Bush fans. She seemed, in certain ways, so current in her embrace of femininity as power—protean, generative, and emotive—and in the fact that, for all her artiness, she also eagerly grabbed onto the contemporary pop sounds and tools that she liked (drums recorded with the heavy-hitting effect called “gated reverb,” which was favored by Michael Jackson and Phil Collins, for instance). She anticipated a busier and more nonchalant traffic between pop and indie music.

Listening to all the tracks on a complete boxed set is like going to a party and talking to all the strangers you’d normally avoid instead of the friends you already have. I’d pretty much skipped “The Dreaming,” for instance, the album that came out in 1982, and is regarded, dimly, as a dry run for her masterpiece, “Hounds of Love.” On the title song, a droning soundscape about the destruction of aboriginal lands, Bush makes the ill-advised decision to sing in an Australian accent. On the bouncy ska number “There Goes a Tenner,” about a failed bank heist, she makes the ill-advised decision to sing in a Cockney accent. The bizarre vocal gymnastics of “Get Out of My House,” a song inspired by Bush’s reading of “The Shining,” include hee-hawing like a demonic donkey.