If USD was to go away tomorrow how would you know how much a Bitcoin is worth?
Euros, Yuan, gold, rubles?
I think the OP was referring to an increase in Bitcoin's value, not the dollar's collapse, although both are probably inevitable to some degree.
What if there was no more gold or silver or fiat money, How would you determine Bitcoins value then?
Very simply, it would be the sum total of all the goods and services produced in the economy divided by the total number of Bitcoins in circulation. That's how you determine the value of any currency, with certain complications of course for fiat/fractional reserve banking.
Of course we usually quote value of one currency relative to another. As long as the market has faith in a currency, it isn't dependent on value on another currency, even gold, fiat, etc.