In 1942, she voluntarily applied to the recruiting station of Sadki with a request to be sent to the front and was enlisted as a corpsman in the 15th Mortar Regiment of the 33rd Mortar Brigade. The military unit in which Anna Konstantinovna Bychkova served was included the 2nd Guards Breakthrough Artillery Division and sent to the Southern Front (later renamed the 4th Ukrainian front).
In 1943, she participated in the liberation of Horlivka, Melitopol and other cities in the south of Ukraine.
From the end of 1943 to May 1944, she took part in the liberation of Crimea – assault crossing of the Sivash, crossing the defenses of the Turkish Rampart. In May 1944, she participated in the liberation of Sevastopol. After the end of the liberation operation, the 33rd Mortar Brigade, among other meritorious units that distinguished themselves in the battles for the city, by Order of the Supreme Commander-in-Chief was named
After the liberation of Crimea, the military unit was transferred to the 3rd Belorussian Front, where it took part in the liberation of Belarus and Lithuania.
Order of the Patriotic War, 1st class, medal "For Battle Merit", medal "For the Victory over Germany"