I don’t think bitcoin has been thoroughly studied from a Vinaya perspective. As far as I can see, though, it would be treated like any other form of currency. There are lots of grey areas in the Vinaya when it comes to the use of money. Obviously, the whole culture and use of money was much simpler then. Nevertheless, a few basic principles cover most cases. A monastic should not:
- Own money or similar means of exchange
- Make financial transactions, i.e. receiving or paying money
- Give orders for others to make financial transactions. This would, I think, include making bitcoin transactions.
However, a monastic may give indications short of commands for the use of funds, for example, “I need a new robe, are there sufficient funds for that?”
Generally speaking, it is a good idea to renounce everything when going forth. But this isn’t always possible or advisable, for a variety of reasons. Perhaps someone is not sure if they will remain in robes. Or maybe someone has dependents, or medical costs. Also, the place of ordination matters. Some monasteries will supply all a monastic’s needs, but in other places they don’t, so you have to have your own resources.
In such cases, as suggested by @Gabriel_L , a new monastic may set up a fund to be managed by a trusted lay steward. Typically this will be a family member, good friend, or long term monastery supporter. The funds are legally transferred to the steward, with an understanding, usually informal, that they are to be used according to the monastics’ wishes.
If for some reason this doesn’t work, a monastic may still ordain while owning money. Most of the Vinaya rules on money deal with making transactions, rather than simple ownership. This is, admittedly, a thin excuse and I don’t recommend it. But technically it would be a legally valid way to ordain, and if there was a Vinaya infraction, it would be a minor one. Later the monastic could transfer the funds to a steward, or just give them away.