Career
He lives in Rijeka. Bebek is considered the best Croatian referee and is the only Croatian referee who supervised two Union of European Football Associations Champions League group stage matches (Lazio v Werder Bremen during the 2007-2008 season and Bordeaux v CFR Cluj in the 2008-2009 season). He also refereed at the 2013-2014 Union of European Football Associations Champions League knockout stage (Paris Saint-Germain - Bayer Leverkusen). He has refereed at the 2007 Fédération internationale de football association U-17 World Cup.
He was also a fourth official at Union of European Football Associations Euro 2008.
He refereed at the 2009 Fédération internationale de football association U-20 World Cup and invited to Indian League. He was preselected as a referee for the 2010.
He attracted a wave of criticism during the Europa League 2015-2016 season, where he refereed a match between South Carolina (U.S.) Braga and Fenerbahçe, and made multiple questionable decisions, leading to accusations of "match fixing" and match "bias". One fan even commented on Ivan"s decisions as the "worst refereeing calls in football history".