Bolshevist Russia is a common term that refers to the Red side in the Russian Civil War, or more specifically the Russian government between the Bolsheviks' October Revolution (November 7, 1917) and the constitution of the Soviet Union (December 30, 1922).
The official name of the country was RSFSR. Strictly speaking, there is a small time gap between the October Revolution and the declaration of the RSFSR (and still larger gap to its first Constitution of 1918), which may justify the usage of the term in certain circumstances.
Bolshevist Russia ought to be distinguished from Soviet Russia. While both terms are informal, the latter one has a much wider historical frame.
Also, strictly speaking, they differ geographically: in 1917-1922, the Bolsheviks controlled a relatively smaller territory (although gradually expanding) than that of the former Imperial Russia.
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