Bajčičák started for the first time in December 1995 in Brusson over 15 km freestyle in the World Cup . At the Junior World Championships in 1996 he was second over 10 kilometers and third over 30 kilometers. He achieved his first World Cup points in January 1997 over 10 km classic in Hakubo with place 30, the first top 10 place he achieved with rank 7 in January 2001 over 15 km classic in Soldier Hollow . Bajčičák won his only World Cup in February 2005 in Reit im Winkl over 15 km freestyle, and in March of the same year he achieved another World Cup podium with third place at the skiiathlon in Falun . In January 2008 he was also third in a pursuit stage of the Tour de Ski . He was also placed in the top ten a total of four times in the 50 km race on Holmenkollen in Oslo ; his best result there was fourth in March 2005.
His best results at world championships , in which Bajčičák has consistently participated since 1999, were fourth in the skiathlon in Oberstdorf in 2005 and sixth in the 50 km mass start race in classic technique in Sapporo in 2007 .
Bajčičák also competed for Slovakia at the Winter Olympics in Nagano , Salt Lake City , Turin , Vancouver and Sochi . He achieved his best placings with sixth place in the 2006 skiathlon and twelfth place over 50 km classic in Salt Lake City and with the Slovak relay in Vancouver.