In 1988 she became the second wife of the Argentine-Israeli pianist Daniel Barenboim. They had met while Barenboim was still married to the British cellist Jacqueline du Pré. By the time Barenboim met Bashkirova, du Pré had been diagnosed with multiple sclerosis. During du Pré's final illness, Barenboim and Bashkirova lived together and had two sons. The younger son Michael is a classical violinist and the elder David is a manager-writer for the German hip-hop band Level 8.
Bashkirova was previously married to the violinist Gidon Kremer.