Spalova started her career in local club in Přerov before moving to play in nearby Olomouc, where she made an impression and got a call for the national team, participating in the 2001 European Championship and the 2002 World Championship. Between 2003 and 2008 Spalova played in France, Turkey and Poland, winning the championship in both Turkey and Poland, as well as the Polish Cup and Supercup. In 2008 Spalova returned to play in the Czech League for VK Prostějov, with whom she won the league championship and national cup in 2009 and 2010. In 2010 she married Tomáš Berger, adopting the name Mila Bergrova, and continued to play with Prostějov, as the club won two further doubles, eventually retiring in 2012. In 2018 Bergrova returned to play for Extraliga club VK Brno.