Her mother preferred to see her daughter on the ballet stage; however, Bessonova decided on rhythmic gymnastics.

[4] In 1999, Bessonova was the youngest in the Ukrainian team during the 1999 World Championship in Osaka, Japan, yet she made such a good impression that the RG specialists wrote her name immediately as a future top gymnast.

She dominated the 2002 World Cup Final in Stuttgart in November, by winning the first place on the hoop, the rope and the clubs.

Bessonova was very close to the all-around title but finished with the silver medal behind Russia's Alina Kabaeva after a drop during her ball routine.

She made her Olympic debut and won the bronze individual all-around medals at the 2004 Athens Olympics with a total score of 106.700 (ribbon 26.725, clubs 26.950, ball 26.525, hoop 26.500) behind two Russians, silver medalist Irina Tchachina and gold medalist Alina Kabaeva.

In 2005, Bessonova became a six-time silver medalist during 2005 World Championships in all-around, rope, ball, clubs and ribbon finals.

The year would also mark the start of a new challenge for Bessonova with rise of new Russian gymnast Evgenia Kanaeva.

In 2008, Bessonova won all-around golds at the LA Lights, Deriugina Cup (Kyiv World Cup) and Miss Valentine Competitions, as well as the all-around silver at the European Championships in Torino behind Russian star Evgenia Kanaeva.

After completing her career in professional sports, Bessonova appeared in Ukrainian television projects.

[8] Back in 2009, Bessonova took part in «Dancing for You» TV show, becoming the winner (partnered with Olexander Leshchenko).

[citation needed] Bessonova's early years are described in the book National Olympic Committee of Ukraine for Rhythmic Gymnastics and Iryna Deriugina, Olexandra Tymoshenko, Olena Vitrychenko, Kateryna Serebryanska, Anna Bessonova (in Ukrainian) (Національний олімпійський комітет України про художню гімнастику та Ірину Дерюгіну, Олександру Тимошенко, Олену Вітриченко, Катерину Серебрянську, Анну Безсонову / текст: Григорія Палія та Олександра Мащенка; відповідальний редактор Олена Мовчан.