Born in a noble family in Odessa, Russian Empire. He graduated in law from the University of Novorossiysk in 1881. That same year he arrived in Bulgaria, appointed to the position of secretary of the Legislative Committee in Eastern Roumelia. There he founded and became the first director of the Plovdiv Public Library, which he organized along the lines of the Petersburg Public Library. He also laid the foundations of the archaeological museum with its various collections, including numismatics. Bashmakov collected and studied Bulgarian folk songs. In 1882 he travelled around Macedonia and delivered a report on Bulgarian folk poetry at the archaeological congress in Odessa in 1884. His study „Болгария и Македония“ (Bulgaria and Macedonia) was published in 1899.
In 1882–1885 Bashmakov was first a lawyer in Odessa, then city justice of the peace and president of the congress of justices of peace in Dubno and what was then called Libau. He took part in the organization and opening of the first in Europe Pasteur Bacteriological station in Odessa in collaboration with Ilya Mechnikov and Nikolay Gamaleya. He maintained a correspondence with Louis Pasteur.
Bashmakov participated in the judicial reform in the Baltics and drafted legislation in the commission preparing the new imperial civil law. A Pan-Slavist and a prominent figure Slavic Movement, he adhered to the ideology of nationalist monarchy.
In 1898 he was appointed juristconsult at the Ministry of Foreign Affairs and began studying the situation in the Balkans. In 1899 he travelled across Bulgaria and Macedonia where the situation was quite tense. His travels provided material for articles in which he described the deplorable situation of Macedonian Bulgarians. In 1904–1905 he was editor-in-chief of the official Foreign Ministry diplomatic journal Journal de St. Petersburg which was published in French. On 1 October 1905 he bought the publishing rights of the „Военное время“ (Military Times) newspaper and changed its name to „Народний голос“ (Popular Voice). During the revolutionary events in 1905–1907 he repeatedly spoke of the need of determined resistance to revolutionary forces and then established the Russian Popular Centre party. He was an active participant in the First All-Russian Congress of Soviets on 8-12 February 1906 in Petersburg and in the Second All-Russian Congress in 6-12 April 1906 in Moscow. The membership of the new party featured intellectuals such as Platon Kulakovskiy, Nikolay Shipov, Nikolay Kuznetsov, Pavel Mansurov and others. At that time, he became member of the Russian Sobranie and in 1908 was one of the initiators of the establishment of the Society of Russian Outlands.
On the initiative of Pyotr Stolypin he was appointed editor-in-chief of the Government Gazette, a position which he held until 1913.
After the October Revolution in 1917 he was assistant to the Chief Red Cross Officer with General Anton Denikin. In 1919 he emigrated, first to Turkey and then to Serbia. Then he moved to France in 1924. As an émigré he worked in the field of ethnography and read lectures at the Chair of Black Sea Paleontology with the French School of Anthropoly and the Institute of Human Paleontolog. He died in Paris in 1943 and was buried at the Sainte-Geneviève-des-Bois Russian Cemetery.
Foreign member of the Bulgarian Academy of Sciences (1902).
Bashmakov was the author of works on Bulgarian history, folklore and law. He wrote under the pen name of Veshchyi Oleg.
- Виды крепостничества в Болгарии в турецкую эпоху. – Юридический вестник, 1885, № 6–7, 436–448.
- Болгария и Македония: С иллюстрациями, по фотографиям, снятым на месте и с картой Западной Македонии. Санкт Петербург, 1903.
- Балканские речи. Санкт Петербург, 1909.
- Енциклопедия България : Т. 1. София, 1978, с. 231.
- Мосенгов, Атанас. Александър Александрович Башмаков : Дейност в Пловдив. – Библиотекар, 1974, № 7–8, 53–54.
- Радев, Симеон. Строителите на съвременна България : Т. 3. София, 2009, с. 243.