Baudyšová joined the Czech national women's curling team as the alternate in 2013. Her first international event was when the team played in the 2014 World Women's Curling Championship where the Czech Republic went 3–8. In 2016 they played in the 2016 Europeans and finished in fourth place, which also qualified them for the 2017 World Women's Curling Championship. There, they finished with a 5–6 record. At the 2017 Euros, they finished with a 3–6 record, qualifying once again for the World Championship. At the 2018 World Women's Curling Championship, the Czech team qualified for the playoffs for the first time with a 6–6 record. They then lost the qualification game 7–3 to Russia's Victoria Moiseeva. The 2018 Europeans were not successful for the Czechs as they did not qualify for the World Championship. The following season, they would qualify for the Worlds, after going 3–6 at the 2019 European Curling Championships. The 2020 World Women's Curling Championship was cancelled due to the COVID-19 pandemic, but the team represented Czech Republic at the 2021 World Women's Curling Championship which was played in a bio-secure "bubble" to prevent spread of the virus. There, they finished in twelfth place with a 3–10 record.