Bj?s musical career began at the age of eleven, when she began studying classical piano in elementary school. One of her instructors submitted a recording of Bj?singing Tina Charles' song "I Love to Love" to Radio One, an Iceland radio station. The recording was aired nationally; upon hearing it, a representative of the record label Fį¬«inn contacted Bj?with a record contract offer. With the help of her stepfather, who played guitar, she recorded her first album, eponymously entitled Bj? in 1977, which featured several Icelandic children's songs, and covers of popular songs such as the Beatles' "Fool on the Hill", sung in Icelandic. The album became a smash hit in Iceland, though it was virtually unknown elsewhere.

Punk music began to have an influence on Bj? at the age of fourteen, she formed the all-girl punk band Spit and Snot, shortly followed by a jazz fusion group called Exodus in 1979. In 1980, she graduated from music school at the age of fifteen, and in 1981, she and Exodus bassist Jakob Magn? formed another band, Tappi Tķ«”rrass (which means "Cork the Bitch's Ass" in Icelandic), and released an extended single, Bitiš ¦”st ķ ¶itiš ©® the same year. Their album Miranda was released in 1983.

Bj?next collaborated with Einar Ö²n Benediktsson and Einar Melax from Purrkur Pillnikk, and Guš¬”µgur Ó“tarsson, Sigtryggur Baldursson and Birgir Mogensen from Ž„yr. After writing songs and rehearsing for two weeks, they (under the name KUKL which means "sorceror" in Icelandic) found they worked well together, and decided to continue, developing a sound that some have described as resembling Goth music. Bj?began to show indications of what would become her trademark singing style, punctuated with howls and shrieks.

KUKL toured Iceland with UK anarchist band Crass, and later visited the UK in a series of performances with Flux of Pink Indians. The band produced two albums as a result of these collaborations: The Eye in 1984, and Holidays in Europe in 1986, both on Crass Records. In the summer of 1986, several members of KUKL went on to form a band called Pukl but soon changed the name to Sugarcubes.

The Sugarcubes' first single, "Ammꬩ" (or "Birthday" in English), became a huge hit in England. They gained a significant cult following in the US and UK, and calls from record companies began coming in. Eventually the band signed with One Little Indian in the UK and with Elektra Records in the United States, and recorded their first album, Life's Too Good, in 1988. The album propelled them into international stardom--the first Icelandic rock band to achieve such popularity. While with the Sugarcubes, Bj?participated in a number of side projects. She recorded Gling-Gló¬ ” collection of popular jazz and original work, with the bebop group Trio Guš­µ®dar Ing󬦳sonar, released in Iceland. Bj?also contributed vocals to 808 State's album Ex:El, a collaboration which cultivated her interest in house music.

Tensions steadily mounted between Bj?and Einar Ö²n, however, and by 1992 the Sugarcubes dissolved. Bj?moved to London and began thinking about a solo career; to this end, she began working with producer Nellee Hooper, who had produced for Massive Attack, among others. Their partnership produced Bj?s first international solo hit, "Human Behaviour". Her solo debut album, simply entitled Debut, was released in June of 1993 to positive reviews; it was named album of the year by New Musical Express, and eventually went platinum in the United States. Debut was a mix of songs Bj?had written since she was a teenager as well as newer lyrical collaborations with Hooper.

The success of Debut led her to collaborate with other artists on one-off tracks; she worked with David Arnold on "Play Dead", the theme to the 1993 film The Young Americans (which appeared as an extra track on a re-release of Debut) and also appeared on a track on the 1997 album Not For Threes by Plaid, which was released on the cult Warp Records label.

Bj?returned to the studio during 1994 to work on her next solo album with Nellee Hooper, Tricky, Graham Massey of 808 State, and electronic music producer Howie B. The album, Post, contained songs based on Bj?s relationships and songs about love (one of her favorite subjects), as well as some angry and confrontational material. Like "Debut," it was a collection partly made up of songs she had written in past years.

She wrote the song "Bedtime Story" for Madonna's 1994 album Bedtime Stories, which became Madonna's first single released in 1995 and performed on MTV Unplugged during this time. By 1995, the new album Post was ready; it was released in June, reaching number two on the UK's pop charts, and also went platinum in the United States. January of 1997 saw the release of Telegram, an album of uncharacteristic remixes of songs from Post.