Bocharova competed for "Budivelnyk, Kyiv (Stroitel, Kiev)", debuting at the Nationals in 1948, where she placed fourth on the uneven bars and balance beam. These two were her best events throughout the career. She won the all-around titles at the USSR Championships in 1949 and 1951, with Maria Gorokhovskaya being her main rival. In 1952 Bocharova competed in the 1952 Summer Olympics, the first Olympics for Soviet athletes. Placing 2nd to Gorokhovskaya in the all-around, she won the gold on the beam and contributed to the team's gold. She also earned another silver medal in the team exercise with hand apparatus event. At age 30 she competed in the 1954 World Artistic Gymnastics Championships, winning the gold medal in the team competition, and finished her career afterwards.