Bibic grew up in a family where the accordion was part of everyday life. He began to perform in public at the age of 16, and two years later he was leading Begnagrad. Attempting an ambitious fusion of East European folk, jazz, and circus music, this group followed a similar path as Sweden's Samla Mammas Manna and Italy's Stormy Six. The group toured the Yugoslavian republics, made a trip to Switzerland, released its only LP in 1982, and disbanded a year later (two more albums of archival material came out afterward). After a hiatus during which he worked on film and dance scores, Bibic resurfaced in 1987 in Nimal, a group including ex-Débile Menthol members Momo Rossel and Jean-20 Huguenin (both Swiss), plus Tom Cora and Pippin Barnett (both American). Viewed by many as a Rock in Opposition supergroup, Nimal enjoyed a short but eventful career, releasing two albums, touring Europe's new music festivals, and making one North American appearance at the 1988 FIMAV festival. The group disbanded in 1991.
Another episode of dance scores followed for Bibic, interspersed by short trips to Switzerland and his first solo concerts, all over a backdrop of political turbulence in Yugoslavia, which made any artistic activity very difficult. In 1995, Bibic released his first solo effort, Bratko Bibic the Madleys of Bridko Bebic, on Rossel's imprint LabelUsineS. The album featured ex-Begnagrad clarinetist Bogo Pecnikar. Violinist Matjaž Sekne completed this first edition of the Madleys, but the group was put on hold when Bibic joined Slovenian-American Guy Klucevsek's Accordion Tribe, an accordion ensemble also featuring Finland's Maria Kalaniemi, Austria's Otto Lechner, and Sweden's Lars Hollmer (of the Samlas). A European tour, a critically acclaimed debut CD, and another visit to Canada later, Bibic got back to his Madleys, recruiting Begnagrad's old rhythm section Nino de Gleria (bass) and Aleš Rendla (drums) to record Na Domacem Vrtu (In the Family Garden), a soundtrack for a silent film made of historic archives and edited by the accordionist.
Besides appearing on two more Accordion Tribe albums, Bibic also performed solo and in duos with Lechner, Sekne, and Wädi Gysi. In 2009, the Bergtöne label released Live at Alpentöne, a recording made by a new version of Bratko Bibic the Madleys (consisting of Bibic, violinist/violist Sekne, saxophonist Vasko Atanasovski, clarinetist/flutist Boštjan Gombac, and drummer Marjan Stanic) at the 2007 Swiss Alpentöne festival in collaboration with Swiss ensemble Rämschfädra and Canadian-born, Switzerland-based multi-instrumentalist Shirley Anne Hofmann (who played euphonium). Another Bratko Bibic the Madleys album, Kabinet cudes Brutka Bimbica (aka Cabinet of Wonders of Brutko Bim-bitch), was released by the Slovenian Klopotec label in 2013. The album featured new Bibic compositions recorded at Ljubljana, Slovenia's Kino Šiška Center for Urban Culture in December 2011 by a Madleys lineup featuring Bibic, Sekne, Atanasovski, Gombac, and new member trombonist Uroš Polanc, along with guest musicians including Lechner. Also included on the album were selections from a 2010 Madleys club show, in which the group performed improvisations with nonsensical vocals and sampling, all inspired by Dante's The Divine Comedy. ~ François Couture, Rovi