A Ponzi scheme is characterised as follows (this is according to Wikipedia, rather than for example the US Department of Justice, which would focus more on the criminal culpability in its definition):
A Ponzi scheme is a fraudulent investment operation where the
operator, an individual or organization, pays returns to its investors
from new capital paid to the operators by new investors, rather than
from profit earned by the operator.
If you sell your holding in Bitcoin (or any asset) to another investor, then you aren't being paid a return by the operator of the scheme at all, from new capital or otherwise. The concept is not applicable.
A Ponzi scheme is when the operator claims that they're holding people's money and using it to generate profit (that is, buying and selling something that generates profit, such that the operator has capital value to match or exceed investor's subscriptions). But actually the operator isn't holding anything, and has given away all the investor's subscriptions.
If Bitcoins paid interest/dividends in US dollars, meaning that you could keep your Bitcoins and take a return, and furthermore if the interest was paid using new subscriptions, then Bitcoin would be a Ponzi. But nothing like that happens at all.
Bitcoin isn't an investment scheme that holds your money for you. It is, as the other answers say, a tradable commodity. So, statements like "thus there is $1000 in the Bitcoin economy" doesn't mean that some hypothetical operator is holding $1000 in a US dollar-demonated bank account, and that it uses this money to pay anyone who wants to cash out. Nothing of the sort. If the price goes to $200 and those 10 people cash out, all that means is that 10 other people want to pay $200 each for bitcoin, and have bought them from the first 10 people. There isn't "$2000 in the system", the original owners have taken $2000 from the new owners. However, the value of the 10 bitcoins at the time of the trade is $2000, so the bitcoin system as a whole is described as "being worth $2000". Sometimes people say it "has $2000 in it", but this means it has $2000 worth of bitcoins in it, not that there are 2000 actual dollars in there. There is no guarantee as to what the value will be when the new owners sell, and there aren't $2000 "in it" any more than there are really $2000 "in" an old vase you fetch out of the attic and someone on Antiques Roadshow says it's worth two grand.
What Bitcoin (or any tradable asset) can be subject to is bubbles:
An economic bubble ... is "trade in high volumes at prices that are
considerably at variance with intrinsic values". It could also be
described as a situation in which asset prices appear to be based on
implausible or inconsistent views about the future
Because it is often difficult to observe intrinsic values in real-life
markets, bubbles are often conclusively identified only in retrospect,
when a sudden drop in prices appears.
Since Bitcoin (like other currencies) is actually intended to be a marker of economic value with no other intrinsic value, one can argue that the US dollar and gold are also subject to extremely long-running bubbles, and Bitcoin should be no different. But at this point the argument becomes semantic, because what one actually cares about is not whether currency "is a bubble" in that sense, but under what circumstances and how badly it might crash.
Anyway, even if Bitcoin does eventually collapse, which is by no means certain, a bubble is not a Ponzi scheme. It does have one property in common, that the last person in before it collapses will lose most of their money.
