I cannot rule out the possibility of paper money to dissappear but it will take more than a century. Most digital currencies including Bitcoin are still in the middle stage and therefore cannot make paper money to dissappear so quickly.
You don't have to rely on Bitcoin to kill off paper money though. Digital fiat will be the end of paper currency long before bitcoin will. Digital fiat already dominated the US economy. Far more value is exchanged digitally than physically, perhaps even more absolute transactions as well.
Some countries I think would or will replace their paper currency with the digital ones that is those countries who are wealthy but to those who are not might just retain their system as their access in this technological advance can't cope up with their living that is they need cellphones or what to connect to internet and proceed with the transactions. It is natural to think that Bitcoin will be the one to trigger the transformation of fiat to cryptocurrency as it is the leading digital coin and much more reputable and advantageous in many aspects which everyone would like but it may or may not be Bitcoin because the can just create a cryptocurrency to be used within the country in order to replace what they have now so the government can control it but not fully control it if you know what I mean so that they can put come taxes on it.