Bošnjak started his professional career at local club HNK Cibalia in the 1996–97 season. He went on to move to Hajduk Split in 2000 and left the club after two seasons for Al-Ittihad Tripoli from Libya, where he spent a season without getting a chance to make a single appearance in an official match. He came back to Croatia by signing with Dinamo Zagreb in 2004. At the club level, he had his biggest personal successes while being named the best player of the Croatian First League in 2000 and becoming the league's top goalscorer in 2006 with 22 goals scored. He transferred to China League One club Chongqing Lifan at season 2011. In March 2012, Bošnjak joined Rijeka. It is reported that Bošnjak has agreed to terms with Brunei's DPMM FC on a transfer in February 2013. on 2014 Bošnjak has agreed to terms with Persija Jakarta.
Bošnjak played for the Croatian national team and collected a total of 14 international caps in which he managed to score one goal. He made his debut for the Croatian team in their friendly match against Slovakia on 16 August 2000 in Bratislava, but subsequently made only one more appearance for the team over a timespan of more than four years before eventually becoming their regular member in 2005 by making six appearances in the 2006 FIFA World Cup qualifying. He went on to score his first goal for Croatia in their friendly match against Hong Kong at the 2006 Carlsberg Cup in Hong Kong and was then also selected to be part of the Croatian squad at the 2006 World Cup finals in Germany, but played at the tournament for only four minutes of regular time in Croatia's second group match against Japan.