In the popular American imagination, the essence of the Bolsheviks was their leftist political and economic views, but there were lots of other groups around during the Russian Revolution that were just as leftist. What really distinguished the Bolsheviks was their tight party discipline, their rejection of any possibility of compromise, and their constant willingness to purge anyone who didn't slavishly follow the party line.
I'm currently reading a book about Chinese history, entitled Wealth and Power: China's Long March to the Twenty-First Century, which points out how Chiang Kai-shek was enamored with Bolshevism for its party discipline. He was certainly no lefty, but his approach was first to abandon the alliance with the Chinese Communist Party against the Japanese, and then to purge "disloyal" elements of the Kuomintang itself. Of course, the Chinese Communist Party also had periodic purges of any "disloyal" elements. This Bolshevist impulse toward purity above all else, and its rejection of compromise, is fundamentally anti-democratic. And it's the very essence of the Tea Party Republicanism.