Because A: putting a bounty on the leader of a nuclear power is drastically different from the leader of a.. terrorist rebel organization(I'm not entirely sure what to call al qaeda).
And because B: it would change basically nothing. Putin already can't travel in most places internationally because there's an ICC warrant out on him for war crimes. The bounty isn't going to be relevant in Russia or allied places, and it's not going to be much of a motivator to an entire government.
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
(See also EO 12036 and EO 12333 for confirming the policy)
Placing a bounty on Putin would probably violate that EO...
More importantly, the US is really fucking hoping Putin dies of old age or is voted out domestically because direct confrontations may result in Putin pushing ze button and launching ze nukes.
Weird line considering what we're willing to do to nation states to keep their citizens from cooperating socially rather than competing against one another to keep their resource extraction rights open to our capitalists for maximum exploitation.
Who would replace Putin. If you don't know the answer or you don't like the answer any better what is the point. The short list of people likely to replace Putin are no better. (If you put me on the jobs I'd be shot within hours by one of the people on the short list)