 He first came to the attention of the wider footballing public when Rot-Weiß Erfurt took on Bayern Munich in a DFB Cup tie on 10 August 2008.Coming on as a second-half substitute in what was Jürgen Klinsmann's competitive debut as Bayern coach, Bunjaku put two goals past the record champions, who eventually squeezed past their lower-league opponents 4–3.On 14 November 2009, Bunjaku made his international debut for Switzerland in the 0–1 home loss to Norway in a friendly match after coming on as a substitute for Alexander Frei at half time.