In a steady-state system, the price of a monetary asset is given by the "quantity theory of money", which states that:
P x Q = M x V, where
P is the price of the goods, Q is the amount of goods bought by the monetary asset, M is the amount of monetary asset in circulation, and V is the average velocity (the number of times per year that a given bitcoin is used to buy something).
Dump the velocity. and you are good to go. It has to be liquid, the owner needs to know that he can easily get rid of the bitcoins, actual trades are not needed.
You cannot ignore the velocity. If everybody would pay their bills the same day they get the money, instead of waiting to the end of the month, the same amount of trading would require 1/30 as much currency in circulation. If the currency it bitcoin, the smaller demand would imply a lower value per BTC.
Moreover, the creation of virtual forms of the currency is inevitable. I could pay a merchant with a signed paper "I owe you 10 bitcoins, payable in 10 days", and the merchant can pay his supplier with that paper, if they trust me. We could deposit all our bitcoins in a "bitcoin bank", and pay each other with checks from those accounts. Such virtual bitcoins would reduce the demand for actual bitcoins.
There is indeed an initial "free" transfer of value from the whole economy using bitcoin in the end steady state towards two classes of people:
- those who give out the first time a bitcoin (the miners). This is called seigniorage. It is what central banks are good at: printing new money and cashing in on first distribution of it.
- the "early adopters" who stored value in bitcoin before its market value reached B. This last thing is something that has probably not been witnessed since gold became money in the early days of history.
The second case has happened with many private currencies in the past, such as Platinum Pieces of the World of Warcraft game (is that right?), Second Life's Linden Dollars, and, presumably, the Liberty Dollar.
In the first case, the central banks are supposed to use the wealth that they take from the people through seignorage for the benefit of the people. That makes the practice acceptable to the majority of the population. (Whether the governments actually use that wealth for the people's benefit is a separate issue.) With private money like bitcoin, seignorage transfers wealth from the general population to the private individuals who created the currency. In the case of bitcoin, some seigneurs expected to suck in trillions of dollars that way.