At the age of 15, Bucik first took part in FIS races in December 2009 , and in February 2010 at the European Youth Olympic Festival in Szczyrk . She celebrated her first victory in an FIS race in December 2009. Shortly thereafter, the first appearances in the European Cup followed , but remained without any noteworthy results. It had its premiere in the World Cup on January 16, 2010 in the giant slalom in Maribor , where it did not finish in the first run. The first point win in the European Cup took until February 2011 to come. In March 2011 she won a Slovenian championship title for the first time, that in the super combined .
There was a growing trend towards specialization in the technical disciplines of giant slalom and slalom . At the Junior World Championships 2012 in Roccaraso , Bucik won the gold medal in the team competition . On November 26, 2012, she was on the podium for the first time in a European Cup race when she finished third in the Vemdalen slalom . After several good results at the beginning of the 2014/15 season, she was given another opportunity to start in the World Cup on December 13, 2014: in the slalom of Åre , she finished 26th with the high starting number 55 and thus won World Cup points for the first time.
On January 6th and 7th, 2016, she achieved her first victories in the European Cup when she won a slalom twice in a row in Zinal . Over the course of the 2016/17 season, Bucik gradually approached the world's best. With seventh place in the Maribor slalom on January 8, 2017, she achieved a top 10 position in a World Cup race for the first time. On January 26, 2018, she drove to a World Cup podium for the first time in the Alpine Combined in Lenzerheide .