Bukinik was born in 1872, in Dubno in the area of Rivne, which is in today's Ukraine (about 400 km west of Kyiv).
Among his fellow students were well-known musicians such as Ferruccio Busoni, Alexander Scriabin and Sergei Rachmaninoff.
After a brief stay in Berlin, Bukinik came to Saratov in 1899, where he remained until 1904 as a teacher at the Mariinsky Institute.
At the same time, he met with the famous painter Victor Borisov-Musatov, who became his lifelong friend.
In 1901, together with Borisov-Musatov, the field doctor and writers Vladimir Stanjukowitsch, and his wife Nadezhda, he founded the so-called English Club of Saratov.