If the dollar collapses it will be because people no longer think that the US can continue to back it, e.g. because we are too far in debt, we are too corrupt, etc.
There is no backing at all to BitCoin. It is just an algorithm that determines how many BitCoin's will be available on such and such a date.
It may work out if enough people believe in it (e.g. emperor's new clothes.) It may especially work out if important folks have made huge bets on it and something happens to make unloading BitCoin's very difficult.
What's most likely going to happen is that around the time BitCoin reaches its peak government's around the world will accept BitCoins as payment. Those who have the BitCoins will sell them off slowly to governments and the last suckers who will end up holding worthless currency.
That’s how I look at it.