Keep in mind that Bin Laden was responsible for an attack against USA citizens and infrastructure. Putin did a lot of shit to several of Russia's neighbors (Ukraine is just the biggest target), spied on several countries, but never openly attacked USA territory, citizens or soldiers, nor that of any NATO allies.
If the USA did put a bounty on him, it's likely Putin and Russia would receive public support from currently neutral countries, because here goes USA playing world sheriff, pretending to own the entire fucking place and ignoring nations' rights to sovereignty again