All that's left is for BIT shares (which trade at ticker symbol "GBTC") to be moved into shareholders' brokerage accounts, a process that should be finished by next week, and "then it's up to them if they will sell," Silbert said.

The BIT—which cannot technically be called an exchange traded fund because it does not yet have Securities and Exchange Commission approval—received the go-ahead from the Financial Industry Regulatory Authority to trade on the over-the-counter markets. But while these exchanges may conjure up images of boiler rooms and penny stocks, the BIT will be on the higher-standard OTCQX marketplace.

Read MoreBitcoin's golden moment: BIT gets FINRA approval



There are about 1.4 million BIT shares outstanding, and about half of them have been held for more than a year, Michael Sonnenshein, Grayscale's director for sales and business development, told CNBC.

Although trading has not begun for the fund, there are already several pending orders, Sonnenshein said, with the lowest bid at $20 and the highest topping $35. The latter offer would value a bitcoin at more than $350. The cryptocurrency traded around $244 Monday afternoon.

"That's a pretty meaningful premium," Silbert said, explaining that the business model calls for the share price to eventually come closer to reflecting the trading price of bitcoin. For now, however, he said he expects that investors will be willing to pay some premium for BIT shares because it offers them ease of use and storage.