As long as there is a state, there is a ruling class. The question is which class is in the ruling position - the bourgeoisie or the proletariat. The USSR had democracy - there were voting structures up and down the entire structure of the union. There was no bourgeoisie class before the revisionists under Kruschevi liberalized. The only clas available to rule after the revolution was the working class.
Anarchists like to claim that "ruling class" is a class, but it's not. It's a role that a class plays. By removing the bourgeoisie class from the role of ruling class and replacing it with it with the proletariat, the proletariat becomes the ruling class.