Bykovsky was a keen sportsman:

Service in the Air Force made us strong, both physically and morally. All of us cosmonauts took up sports and PT seriously when we served in the Air Force. I know that Yuri Gagarin was fond of ice hockey. He liked to play goal keeper. Gherman Titov was a gymnastics enthusiast, Andriyan Nikolayev liked skiing, Pavel Popovich went in for weight lifting. I don't think I am wrong when I say that sports became a fixture in the life of the cosmonauts.

He was married to Valentina Mikhailovna Sukhova; they had two sons. He died on 27 March 2019.