Russia Bounty Response Act of 2020 This bill requires various actions in response to the influence of Russia's government in South and Central Asia and contains other related provisions. The Department of State shall report to Congress a strategy for using U.S. diplomacy to counter such Russian influence. The bill imposes sanctions on various individuals and entities, including (1) Russian President Vladimir Putin or any person acting on his behalf, (2) any senior Russian government official involved in a program to provide bounties for killing members of the U.S. Armed Forces or certain North Atlantic Treaty Organization (NATO) forces in Afghanistan, and (3) individuals and entities that facilitate illicit or corrupt activities on behalf of Putin or other specified persons. The bill imposes civil and criminal penalties related to violations of such sanctions. The bill also authorizes various activities, including (1) rewards for information about Russian bounties against U.S. Armed Forces anywhere in the world, and (2) State Department activities to counter Russian influence in South and Central Asia. The State Department shall seek to establish a working group involving officials from the government of Afghanistan to address threats to Afghanistan's security posed by Russia's government. The State Department must also create a Deputy Assistant Secretary position tasked with coordinating efforts to counter Russian influence in South and Central Asia. The President shall also appoint a special envoy tasked with countering Russian influence in the region.