"It's something regulators need to deal with but not ban," Bair told CNBC's " Fast Money " on Thursday. Bair, who said she does not own any bitcoin, now serves as a board member for Paxos, a financial firm developing blockchain technology for digital currency.
"I think some additional regulation would be good, and I argue for that," she said. "Especially on anti-money-laundering laws, where I think there are a lot of concerns over use of bitcoin or other digital currencies."
The former U.S. Federal Deposit Insurance Corporation chair served under President George W. Bush during the financial crisis in 2008.
Bair said bitcoin and other digital currencies could benefit from more scrutiny to ensure there is no manipulation or fraud and that there are clear disclosures so that people can make informed decisions when investing.
But banning the asset, she said, would be a mistake.
"We don't ban assets," she said. "Where does that stop?"
"There are a lot of products out there that ... in a lot of people's minds have questionable value," she said. "But ... traditionally in the U.S. we've let markets price values and determine what the value is."
Cryptocurrencies fluctuated rapidly this week over regulatory concerns and South Korea' s announcement that it was considering banning digital currency, sending investors into a tailspin and triggering sell-offs. So far about a dozen countries — including France , Bolivia and Russia — have proposed a ban on cryptocurrencies or already have one.
The unpredictable market, of which bitcoin is the most popular digital currency, lost approximately $200 billion as a result of the sell-offs. That represents a third of its value since peak trading in mid-December. Once valued at approximately $19,500 per coin, bitcoin's worth fell below $10,000 on Tuesday.
By Thursday, bitcoin and other cryptocurrencies — including ripple, ethereum and litecoin — were on the upswing once again. Bitcoin briefly topped $12,000 on Tuesday, an increase of more than 30 percent from the day before. But prices were still down more than 40 percent from peak December prices.
Cryptocurrency's volatile nature and potential for large-scale gains could be what attracts some market watchers.
Bair's biggest concern, she said, is that people are investing in something they don't understand.
"I worry that people are getting into this because they're seeing the skyrocketing returns and the tremendous increase in value without really understanding what it is," she said.
— CNBC's Evelyn Cheng contributed to this report.