 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.He was part of the Swiss squad for the 2010 FIFA World Cup, playing the last 13 minutes of the group match against Chile after coming on for Gelson Fernandes.