Having previously represented Switzerland, participating at the 2010 FIFA World Cup, he switched to the newly formed Kosovo national team.

The team won promotion to the Super League in 2003–04 and over the course of the next 18 months the young forward made 39 top-flight appearances.

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.

[2] On 14 November 2009, Bunjaku made his international debut for Switzerland in the 1–0 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.