The debate over the COVID-19 pandemic is constantly trending at online conversations since its beginning in 2019. The discussions in many social media platforms is related not only to health aspects of the disease, but also public policies and non-pharmacological measures to mitigate the spreading of the virus and propose alternative treatments. Divergent opinions regarding these measures are leading to heated discussions and polarization. Particularly in highly politically polarized countries, users tend to be divided in those in-favor or against government policies. In this work we present a computational method to analyze Twitter data and: (i) identify users with a high probability of being bots using only COVID-19 related messages; (ii) quantify the political polarization of the Brazilian general public in the context of the COVID-19 pandemic; (iii) analyze how bots tweet and affect political polarization. We collected over 100 million tweets from 26 April 2020 to 3 January 2021, and observed in general a highly polarized population (with polarization index varying from 0.57 to 0.86), which focuses on very different topics of discussions over the most polarized weeks-but all related to government and health-related events.