1917, from Russian bol'shiy "greater," comparative of adjective bol'shoy "big, great" (cf. Bolshoi Ballet), from Old Church Slavonic boljiji "larger," from PIE root *bel- "strong" (cf. Sanskrit balam "strength, force," Greek beltion "better," Phrygian balaios "big, fast," Old Irish odbal "strong," Welsh balch "proud;" Middle Dutch, Low German, Frisian pal "strong, firm").
It was the faction of the Russian Social Democratic Worker's Party after a split in 1903 that was either larger or more extreme (or both) than the Mensheviks (from Russian men'shij "less"); after they seized power in 1917, applied generally to Russian communists. Bolshevism is recorded from 1917.
The radicals in the Russian Revolution, who were led by Lenin and who favored revolution rather than gradual democratic change.
Note: Bolshevik has been used as a general term for a radical leftist or for a communist of the Soviet Union.