[7] At the March 2013 Junior European Epee Championships in Torun, Poland, he won a silver medal in team épée.

At the 2018 European Fencing Championships in Novi Sad, Serbia, in June, he won a gold medal in team épée.

At the 2018 World Fencing Championships in Wuxi, China, in July, Bida won a bronze medal in team épée.

[7] In March 2019 at the Buenos Aires Fencing World Cup in Argentina, Bida won the gold medal in individual épée.

[8][11][2] At the January 2020 Fencing Grand Prix in Doha, Qatar, he was the top seed and won the gold medal in individual épée defeating 2019 French team world champion Alexandre Bardenet 15-6 in the final, and that same month at the Heidenheim World Cup in Germany, he won a bronze medal in individual épée.

[14] In recognition of his achievements at the Tokyo Olympics, Bida received the Order "For Merit to the Fatherland" first class from the president of the Russian Federation.

[5] In May 2023 Bida left Russia and moved to the United States to embark in a career there, joining the AFM (Academy of Fencing Masters) Coaching Team in northern California.

"[16] The couple now lives in a one-bedroom apartment, as they await the birth of their first child, and teach children at the local fencing club.

[8][17] He and his wife join Konstantin Lokhanov as Olympic fencers who left Russia to go to the United States after the 2022 Russian invasion of Ukraine.

[18][19] The reaction of the Russian Fencing Federation changed dramatically once Bida publicly denounced Russia's invasion of Ukraine, and followed that up by winning a gold medal at the U.S. Summer National Championships.

[25][16] Days later, the United States Olympic & Paralympic Committee (USOPC) and USA Fencing both wrote letters in support of Bida, his wife, and Lokhanov being granted U.S.

[8] USOPC CEO Sarah Hirshland wrote as to the fencers, in a January 4, 2024, letter: "Our intention in endorsing their cause is to enable them to proudly represent our remarkable nation in the upcoming 2024 Olympic Games and other forthcoming international competitions.

"[8] Phil Andrews, the CEO of USA Fencing, wrote in a January 5, 2024, letter to the U.S. Congress: "All 3 of these individuals have made sacrifices at great personal cost, and put their lives at risk to be able to represent our nation, and we ask you to make every effort to support them in the extraordinary circumstance.

"[28] Russian State Duma deputy Vitaly Milonov called the fencers "cowards, traitors, and defectors" and "political rags.

[15] Pravda shed light on the Russian officials' reaction, writing: "It is difficult to overestimate the propaganda value of sports, but "defectors" influence public opinion no less.

[2][5] Bida was originally set to follow in his grandfather and uncle's footsteps in competitive water polo; however, he contracted a severe case of sinusitis when he was 12 years old that prevented him from getting in the pool.