In March 1774, Bibikov forced Pugachev's rebel army to abandon its siege on the city of Orenburg.

In the letter to Catherine II of Russia, he wrote: "I expect from v. V. of the resolution of the boundary local matter not on the Polish statutes, but the zbornomu (cathedral) packing code".

During this campaign Bibikov fell ill with cholera and died, aged 44, Empress granted a large estate to its family.

All data attest to the fact that Bibikov connected the bright military and administrative abilities, large diplomatic time with the independence of persuasions and the incorruptible honesty.

His son from his marriage with Princess Anastasia Semyonovna Kozlovskaya, Aleksandr Aleksandrovich Bibikov, served as a military commander in the Napoleonic Wars, and held several diplomatic posts.