graduated with distinction in symphony and opera conducting from the class of Jan Wincenty Hawel at the Music Academy in Katowice. Between 2006 and 2013, he was artistic director of the Karol Szymanowski Academic Symphony Orchestra in Katowice. He is also a graduate of the Music Academy in Cracow, where he studied the oboe with Jerzy Kotyczka. On a scholarship to Siena's Accademia Musicale Chigiana, he has perfected his métier in the class of Gianluigi Gelmetti (2001) and Lothar Zagrosek (2002, diploma with honours). He has also participated in conducting masterclasses run notably by Gabriel Chmura, Kurt Masur, Zoltán Peskó, and Pierre Boulez.
He won the 1st Prize at the National Review of Young Conductors in Białystok (1998) and two special prizes at the Grzegorz Fitelberg International Conducting Competition in Katowice (1999), and has held several scholarships form the Polish Ministry of Culture.
He is the permanent conductor of the OMN New Music Orchestra, which he has directed at various modern music festivals including Warsaw Autumn, Wrocław's Musica Polonica Nova and Musica Electronica Nova, Poznań Music Spring, Bratislava's Melos-Ethos, Lviv's Velvet Curtain 2, Paweł Szymański Festival in Warsaw, Beijing Modern, and the Hindsgavl Festival in Denmark. He has given over 100 Polish and world premieres. With the OMN, he has made numerous recordings for Polish Radio, winning a Fryderyk nomination in 2003. For his monographic record with the works of Weronika Ratusińska, he won the Pizzicato Supersonic Award (2009). The recording of Paweł Szymański's Three Trakl Songs received a recommendation at the International Rostrum of Composers in Paris, while Magdalena Długosz's Gemisatos (with Sinfonia Varsovia) and Ewa Trębacz's things lost things invisible (conducted at 2007 Warsaw Autumn in partnership with Arturo Tamayo) were recommended in 2009. Bywalec's CD with cellist Jakob Kullberg, featuring the cello concertos by Nordic composers (Nørgård, Nordheim, and Saariaho) won the Danish Radio's Lyt til Nyt Prize in 2013. In 2016, a CD with clarinettist Michelle Marelli was published by Decca.
From 2011 Szymon Bywalec has sat on the programme committee of Warsaw Autumn Festival, and was artistic director of the Musica Polonica Nova festival in 2013-16. He has conducted many philharmonic, radio, and chamber orchestras in Poland and other countries.