There are at least two definitions of a speculative bubble. The first, and most widely accepted, is that it involves a price of an asset that rises substantially above its fundamental and then falls back towards that fundamental. The other, not necessarily all that clearly distinguishable from the former, involves an asset price that rises due to people buying due to an expectation that they will get a capital gain from its expected future price rise, with this then happening due to a self-fulfilling prophecy, with eventually the price falling sharply, with this not necessarily involving a fall towards a fundamental because the asset may have no fundamental at all.
I note before proceeding futher that there is an enormous debate and literature on identifying fundamentals at all, even when they might theoretically exist. There is a serious body of opinion dating from Flood and Garber a quarter of a century ago that one cannot identify them econometrically ("Tulipmania"). This has been shown to be false by me and many others in various papers, including particularly on closed-end funds where the net asset value of the fund minus taxes and fees is a fundamental, and when those soar to twice the value of the underlying net asset value, well, we are looking at a bubble. The lit is there and decisive. I asked Garber to comment on a paper presented a long time ago at a conference on this point, but the chicken shit did not show up to admit that he was just plain wrong. He had no legitimate excuse for his absence.
Of course Bob Shiller has made pretty reliable estimates regarding housing prices based on price to rent and price to income ratios. His studies of these by 2005 were pretty decisive to anybody who was remotely paying attention (including at the Fed, Janet Yellen, the only one there to take this seriously at the time), that the US housing market was in a serious bubble that was going to crash big time. The matter of forecasting how bad it would get with the Great Recession became a matter of who had figured out how deeply the financing for all that had gotten involved in world financial markets at a fundamental level, and very few did figure that out.
But then there are assets that have no fundamental at all, even theoretically, quite aside from all the horrendous econometric identification problems pointed out by such serious people as Jim Hamilton, for whom I have the deepest respect. The question for cryptocurrencies in general is whether they have a fundamental, and it may well be that they do not. If that is the case, then only the second definition of a speculative bubble may be relevant, and that is much harder to determine than the former, already admittedly a difficult matter.
How might bitcoin have a fundamental? One reason might be for its use as a medium of exchange. However, while it is certainly being used as that, for regular commodity transactions as of now it remains as a sometimes difficult alternative to cash dollars. As near as I know there are no regular commodity transactions in the real economy that require it. So, it may have no fundamental, and from what I have heard, this is widely accepted among the more sophisticated bitcoin traders. This would make it like art, such as the recent sale for $450 million of the possibly faked "Salvator Mundi" supposedly by Leonardo da Vinci. And, of course, there is good old gold that has a long had a value as a store of wealth about an order of magnitude above its likely strictly commercial fundamental value.
However, it may be that bitcoin has a fundamental value above zero, if wildly fluctuating and hard to estimate, far beyond the econometric difficulties identified by people such as Hamilton, much less Flood and Garber. It is that to buy most of the other cryptocurrencies one must use bitcoins to do so. Oh, this is really a gas. The fundamental for one asset is based on its ability to purchase even more lacking in fundamentals and totally speculative assets one must own it. Wow.
Thus we have that any real fundamental for bitcoin is a derived demand for any among the vast universe of other cryptocurrencies, and we should keep in mind that bitcoin itself is horrendously inefficient compared to others because of its accelererating and already very large "mining" costs. As near as I can tell there are only two other cryptocurrencies that have any relation to the real world out of the multitude of crytpos. They are ethereum and ripple. The first has been a matter of much speculation itself, given its potential for writing contracts, giving it a serious possibility of much longer use and actual usefulness in the real world. This may yet occur, although for its future it would probably be better for it if it could be bought directly with cash/dollars from the real world rather than having to use the horribly socially inefficient bitcoin, a bad example of first mover advantage, or perhaps the ultimate proof that the first mover should be sent to last.
Which gets us to the quiet and most obscure member of the crypto world, ripple. This cryptocurrency, which is the hardest to buy of them all, is probably the one with the most serious actual real world use, and thus possibly providing a real foundation for bitcoin to have a fundamental, although I confess at this point that I am not certain to what degree purchasing it does rely on using bitcoins. I know that as of fairly recently one had to use bitcoins to buy ethereum, but I am not sure about ripple, which moves with bitcoin, but probably more weakly than any other of all the cryptocurrencies.
The source of its value is that has been adopted by a significant number of banks for their interbank transactions. This now appears to be firmly established, not to go away whatever happens to bitcoin or any of the other cryptocurrencies. Indeed, the underlying idea of blockchains is clearly a brilliant and useful forward movement in managing financial and economic transactions, assuming that is managed in a reasonable and efficient manner, without me remotely dealing with issues of transparency or legality. But it seems that at least some banks have decided to use ripple, which I understand uses a more efficient mining technology.
So, there may well be a fundamental for bitcoin, despite what I understand to be the current consensus among smartass bitcoin traders. But, of course, that fundie is probably way below the current price, as if that matters at all.
Addendum, 12/2: This has been picked up by Naked Capitalism where some commentators have pointed out that apparently one no longer needs bitcoin to buy other cryptocurrencies, especially ripple and etherium. If anything it is etherium that is being used to buy other cryptos. In any case, that reduces the case for bitcoin having a fundamental greater than zero.