To replace the dollar with bitcoin in the near future seems impossible, we all know that if the USA government is angry it will do everything possible to destroy bitcoin. I think it would be difficult to replace the dollar as long as there is no strong country that legalize bitcoin.
I don't think that bitcoin will replace dollar completley, there are people that don't like technology and don't have any mobile, and these people never will change to bitcoin. I think fiat money will be accepted always.
So the same will happen to fiat money as how cash money is getting replaced by digital transactions? Seems plausible, but still, transaction times seems to me too much of a problem for bitcoin to become widely used for day to day uses.