It is a weekly ritual in the New York art world. Each Sunday afternoon a motley queue of artists assembles outside an unremarkable house in Chelsea, New York. Once inside their work will be judged by the 95-year-old owner, Louise Bourgeois, the most eminent female sculptor alive. The day that I go to observe, a French painting student, a psychoanalyst and lifetime Surrealist doodler, and a man who makes sculptures of crucified frogs are among those bringing work. Visitors have been known to leave in tears after a terse critique.

Bourgeois has been holding these salons for more than 30 years. She no longer gives full interviews, though I was invited to submit questions by e-mail. She told me that she maintains the salon because “it’s a chance to meet artists, writers and poets and see what they’re up to”.

It has evolved into a peculiar institution, part ritual homage (“Louise is the mother,” one woman announced, breathily, when it was her turn to show work), part antique discussion group. We were warned that her responses can be “sometimes salty, sometimes sweet”. But that afternoon Bourgeois sat behind a desk in a white wool cap and an avalanche of overalls, looking like a fragile mushroom, and seemed rarely engaged. A woman held up some drawings for perusal: “Very good, mmmm, very good,” she whispered. It was the most we heard. But the whole thing carried on regardless, encouraged by her assistant, who on that day was Robert Storr, one of the most powerful curators in the world, who had only just flown back from Europe after curating the Venice Biennale.

Next month you may begin to see why people persist in going to her salon when Tate Modern opens the first British retrospective of Bourgeois’s career. Her work has long featured in the collection, and you might remember the huge spider that was installed in the Turbine Hall when the museum opened. This new show will include more than 200 pieces, spanning seven decades. It includes examples of her early abstract wooden constructions, such as The Blind Leading the Blind (1947-49); and small, island sculptures, such as Cumul I (1969). There are also renowned pieces such as the taut, shining, headless, suspended body, Arch of Hysteria, from 1993, as well many lesser-known drawings and paintings. If you want to see what she has produced this year you can go across town to Hauser & Wirth Colnaghi where there is a range of work, including an intriguing series in which Bourgeois has cut and restitched her clothes and cast them in bronze. The Tate’s exhibition may be taking a backward glance, but Bourgeois has no time for contemplating the past: when I asked her what she was most proud of, she answered: “I’m exclusively interested in my latest work.” She is working on a series of drawings and a project in Norway, with the architect Peter Zumthor, “which is a sculpture in memory of the people in the 17th century who were burnt as witches – most were women”.

Bourgeois was born in Paris on Christmas Day in 1911. Her family grew prosperous with a business repairing and reselling 17th and 18th-century tapestries and textiles (Louise would later excel at sewing fig-leafs onto the genitals of cavorting classical divinities). Initially, she studied maths, but soon resolved to be an artist. Her first job was as a retoucher of photographs, but Fernand Léger advised her that she should be a sculptor. Then, in 1938, she met the American art historian Robert Goldwater. The two quickly married, and in a matter of weeks they left for the US, where Bourgeois has lived since.

Although little is known about Bourgeois’s marriage, it seems to have been harmonious (they had two children and adopted a further child).

However, in 1982, nearly a decade after Goldwater’s death, and just before she opened her first important retrospective in New York, she announced that her father had had a ten-year affair with her governess, and that her mother had used her as a pawn to monitor his infidelities. “It was child abuse,” she said. She would later claim that her first sculpture was a morsel of bread fashioned into a figure of her errant father and dismembered with a knife. Her mother died in 1932 (“I don’t think I ever recovered from the death of my mother,” she tells me), and her father followed in 1951, upon which, coincidentally or not, Bourgeois ceased exhibiting for 11 years.

Bourgeois has never spoken publicly about her father’s affair before, and some would question her timing, but she has been signalling her emotions for some time through her work. One of the Tate’s exhibits will include an installation from 1974 entitled The Destruction of the Father, which comprises a cave-like hollow, constructed from fabric, wood and latex, packed with red-glowing protuberances. She has talked of it resembling a meal, at which the assembled family finally tire of hearing the father’s satisfied boasts, and cannibalise him.

Yet now, as a personality, Bourgeois seems distant. While making herself available at the Sunday salons, she seems to have slipped into the wings. Storr led the conversations that afternoon, while Bourgeois sat back and ate tapioca pudding. The rest of us sat expectantly forward. Phyllis Krim, a regular at the salon, read some poetry. A student got up and showed some paintings, which Storr splashed with coffee (though it might as well have been holy water as far as the student was concerned).

Finally, chatter about the psychoanalyst’s sketches led to discussion about genius and madness, and the shrink outlined his personal theory about the history of modern art which Storr steamrollered in three seconds. When no one would dare say any more, Storr announced that Louise was tired, and we all went our ways.

Good salon chatter doesn’t exist much anymore outside universities, and I came away feeling that the thirst for it explained why Bourgeois’s institution had lasted so long. I doubted whether Bourgeois had much more to offer herself. But, just a few weeks later, I visited a New York show that proved her continued relevance by placing her work alongside that of Lynda Benglis. A woman a generation younger, Benglis caused an almighty row in the mid 1970s when she published, as an advert in an art magazine, a self-portrait naked, slick with oil and wielding a dildo. It was strong stuff, but Bourgeois would later do something similar, only with more class: in 1982 she posed for Robert Mapplethorpe embracing her 1968 sculpture Fillette, which is basi-cally a two-foot craggy penis. And in that New York show, just across from that picture of Benglis, was a photo of Bourgeois, standing in the hallway of her Chelsea home, wearing a kind of overall swaying with enormous mounds. She looks at the camera as if she knows something that we don’t. She most likely does.

Louise Bourgeois, Tate Modern, Southbank, London SW1 (www.tate.org.uk 020-7887 8888), Oct 10-Jan 20; Louise Bourgeois: New Works, Hauser & Wirth Colnaghi, Old Bond Street, London W1 (www.ghw.ch O20-7287 2300), Oct 10-Nov 17

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