Buki? was given the honour to carry the national flag of Croatia at the opening ceremony of the 1996 Summer Olympics in Atlanta, becoming the 17th water polo player to be a flag bearer at the opening and closing ceremonies of the Olympics.
Buki? is a member of the Croatian Democratic Union. In the 2003 Croatian parliamentary election he attained a seat in the Croatian Parliament. In the 2007 Croatian parliamentary election he retained his seat. His term of office in the Parliament ended in January 2008.
His son is Luka Buki?, who is also a water polo player.