Bogut wuxuu u ciyaaray kooxda Boomers ciyaarihii Olombikada ee Athens 2004, isagoo celcelis ahaan helay 13.7 dhibcood, 9 rebounds iyo 1.2 toogasho oo xanniban iyo toogasho 58.0% garoonka. Wuxuu mar kale u matalayay Australia 2006 FIBA World Championship. Australia waxay u gudubtay wareega 16-ka ka hor inta aysan ka adkaan Mareykanka. Wuxuu celcelis ahaan 12.8 dhibcood ciyaar kasta iyo 6.2 dib u soo celinta ciyaar kasta inta lagu gudajiray tartanka, isagoo hogaaminaya Australia labada qayboodba. Wuxuu u ciyaaray kooxda Boomers ciyaarihii Olombikada ee Beijing 2008. Sanadkii 2012, wuxuu awoodi waayay inuu u ciyaaro Boomers ciyaarihii Olombikada ee London
, maadaama uu horey u jabiyay lugtiisa bidix bishii Janaayo intii lagu jiray xilli ciyaareedkii NBA ee 2011-12.