In the spirit of explaining Bitcoin to Rowling, I dug into some existing work looking into Economics in the wizarding world. I think Rowling understands Bitcoin intuitively. I was amazed to find her description of the economics of wizarding monies starkly similar to crypto-currencies like Bitcoin.

Wizarding monies interestingly exhibit properties of both commodity monies and fiat. They have no non-monetary use value like fiat and like commodity monies, are immune to any tampering.

Economists have long thought of monies as either fiat-like or commodity-like. In 2013 Selgin introduced a new class of monies called "Synthetic Commodity Moneies" which placed monies like Bitcoin somewhere in between the fiat and commodity monies as it exhibited properties of both. This duality is what made Bitcoin unique in the eyes of Economists like Selgin. Wizarding monies too exhibit this duality and would be classified as "Synthetic Commodity Moneies".

It is interesting to note Rowling's description of wizarding monies pre-dates Selgin and even the creation of Bitcoin.

Wizards in the Potterian economy use commodity money. They have three types of coins: gold Galleons, silver Sickles and bronze Knuts, where 1 Gelleon = 17 Sickles and 1 Sickle = 29 Knuts. The coin values are determined solely by their denomination and are independent of their size. The value of a regular Galleon and a foreign Galleon as big as hubcaps is therefore the same (Rowling, 2000, p. 50). The coin values are also independent of the values of the precious metals they are made of. In Rowling (2005), for example, there is an increase in the demand for silver. This, however, has no effect on the conversion rate between the Sickle and the other denominations or on prices nominated in Sickles.
(Rowling 2005, pp. 111 and 117). 

Thus the value of the coins as a medium of exchange in the Potterian economy exceeds their value as a commodity and consequently, although the Potterian money is made of precious metals, its value is determined solely by the trust that the wizards have in the monetary system. Furthermore, unlike commodity money, and like the fiduciary money used in most modern countries, the value of the Potterian money is significantly affected by fluctuations in the wizards’ trust in the monetary system. For example, in Rowling (2005) the supply of goods becomes less reliable because of a war. Consequently, prices go sky high, even though the prices of silver and possibly of other precious metals rise along with the prices of other goods.
(Rowling, 2005, pp. 63 and 111).

The Potterian economy, therefore, seems to function like an economy that uses fiduciary money, with the difference that in the Potterian economy the money is made of precious metals instead of paper. It is possible that wizards use commodity money because they believe that precious metals are more difficult to counterfeit than fiduciary money because precious metals, unlike less valuable materials, cannot be created by magic. 
(Rowling, 2000, p. 67, Rowling, 2005, p. 352, Rowling 2007, p. 240).14

* Potterian Economics - Avichai Snir
* Synthetic Commodity Money - George Selgin