In China, the Bitcoin trade has already been pushed into the underground - the Hong Kong protests are partly financed with Bitcoin. The Russian central bank is now examining how it they are able to censor BTC.
Even though Russia and China are not directly on the drip of the US dollar, the ruble and yuan are based on the same Fiat principle. And so these two nations have an immense interest in censoring free decentralized alternatives like Bitcoin.
In Russia it is being discussed how Bitcoin could be banned. Especially for trade against goods and services a censorship is considered, which is already well advanced. However, there is still a ban on the official definition that applies to the BTC in Russia. Because Cryptocoins are not yet clearly classified as "Money Substitute" - only when this is done, a ban can be made.
But how successful can a ban really be? There is also an active trade in Bitcoin in China. Although this is officially banned there, there are few opportunities for the state to ban trade if it is done anonymously. The same problem will also worry Russia.