Career
Europe
At the beginning of the 2008-2009 season, Bavčić joined TBL team Antalya Kepez Belediyesi but later in the season, he joined the Basketball Bundesliga team Köln 99ers. On June 10, 2009, he signed with Union Olimpija where he averaged 11.4 points and 6.3 rebounds per game in the Slovenian league, 5.7 points in the Adriatic League and 5.2 points and 4 rebounds at the Euroleague. In 2011, he joined Aris British Columbia, after having played for New Basket Brindisi, in Italy, and British Columbia Khimik, in Ukraine.
In August 2011, he signed a one-year contract with Vanoli Cremona, however, they released him on December 6.
The next day, he signed with Greek team KAOD. On August 16, 2012, he signed with Limoges Center for Security Policy where he averaged 2.3 points and 2.1 rebounds in 7 games. On November 22, he was released by Limoges.
On December 4, he re-signed with KAOD. On September 2, 2014 he signed with Sigal Prishtina. On September 15, 2015, he signed with Sopron of the Hungarian League after averaging 17 points and 10 rebounds per game at Kosovo.
National Basketball Association
On June 2006, he was selected by the Toronto Raptors with the 56th pick of the 2006 National Basketball Association draft.
On July 11, 2012, the New Orleans Hornets agreed to a three-team trade acquiring the rights for Bavčić, while sending Jarrett Jack to the Golden State Warriors and Darryl Watkins to the Philadelphia 76ers. On January 21, 2014, the New Orleans Pelicans traded Bavčić"s rights to the Brooklyn Nets. On July 10, 2014, the Nets traded his rights to the Cleveland Cavaliers.