Bajrami was born in Tuzla, Bosnia and Herzegovina, at the time part of SFR Yugoslavia to a Bosniak mother and Albanian father.
She grew up in the nearby village of Mramor where she spent the entirety of the Bosnian War (1992–1995), during which she started singing in kafanas.
The biggest hits from this album are: "Pijanico", "Ljubav si ubio gade", "Život liječi rane", "Mrva hljeba", etc.
After 6 years since the release of this album, in 2010, a demo version of the song “Muška suza” appeared on YouTube performed by Dragana Mirković.
The biggest hits from this album are; “Voli me do bola”, “Bakšiš”, “Rukujmo se kao prijatelji”, “Sarajevo”, etc.
In August 2013, she recorded the comeback song "Nisam ti oprostila" and announced her eighth studio album the following year.
In October 2015, she recorded the first female duet in her career with Enela Palavra; "Mlađe slađe", and the song soon became a hit, especially among the younger audience.
It was followed by "Nisam ti oprostila", "Moje milo", "Tijelo bez duše" and "Samo tvoje oči".
[4][5][6] Bajrami met her first husband, Zoran Vučković from Sarajevo, in March 2003 in the Croatian city of Makarska, where they married six months later.
[9] Selma met her second husband, a Bosnian man named Mujo Musić in July 2011, during a performance of hers at the Modrac Lake by Lukavac.
[20] On 28 February 2010, Bajrami was attending a friends birthday party in Belgrade, when she was attacked and assaulted by a drunk man.
[24] Earlier, Bajrami denied news in September 2008 that she had been attacked by a schizophrenic man with a chainsaw in a nightclub near Srebrenik.