Rothbard repeats this point made by David Hume many times. One place is What Has Government Done to Our Money, pp. 24-26.
For something to become money, it must displace the existing money as the general medium of exchange. People must become convinced that it serves as a general medium of exchange better than any thing else. Of course, government intervention can suppress people’s preferences to choose a market-produced money.
It seems likely, but it’s not logically necessary, that if Bitcoin became money it’s market price would rise. It may be that it’s current price is driven by what proves to be wild speculation.