As long as American economy keeps its leading positions, dollar is unlikely to lose in its value. In the US, Bitcoin is recognized as currency and is being treated as property, which basically means its status is close to the one of the $, only it is a decentralized currency, and thus doesn't have direct ties to the state. When comparing Bitcoin to Dollar, it's possible that with time using Bitcoin will become more prevalent than dollar. But, for example, no currency could completely replace gold from the market during history.
One could suggest Bitcoin won't completely replace dollar, but will be of equal economic power.
Everyone has his own thoughts and ideas about this topic, but I personally feel that after a few years bitcoin will be the mainstream and dollar will die, because people all over the world now change their money in bitcoin rather than dollar, besides till date the situation was different. Now if I want to buy something from another country I will pay from my blockchain wallet,. No need to exchange the money.