Experts said the rise in bitcoin on Tuesday was due to choppy Chinese stock markets which were trading lower for most of the day before closing in mildly positive territory. The Chinese yuan has also fallen against the U.S. dollar this year which has given a boost to bitcoin, according to Bobby Lee, chief executive of BTC China, one of the largest bitcoin exchanges in the world.

The previous 2016 high of $781.31 was achieved in the summer when traders prepared for a process known as "halving" – where the rewards offered to bitcoin miners fall, thus tightening the supply of the digital currency.

People are waking up to the fact that bitcoin is money in the cloud, so when you exchange from local currency like the Chinese yuan or U.S. dollar, you are exchanging this physical money to money in the cloud. What's good about money in the cloud, is it has been stable, the volatility has been down, it's a good store of value," Lee told CNBC by phone.

Other bitcoin advocates have said that the currency is maturing. Peter Smith, chief executive of bitcoin wallet start-up Blockchain, said the market for the digital currency is maturing, and that's reflected in the price movement.

"What we have and in the last four months is consistent week over week growth. This quarter, our consumer business will almost double," Smith told CNBC.

The CEO added that global volatility in geopolitics could also play a part.

"Alternative assets like bitcoin do well when the world is unstable. It looks like the world is getting a lot more unstable," Smith added.

Major financial institutions have been talking about the digital currency world for the past year, but not because of the attraction of bitcoin, but for the underlying technology called blockchain. This is a distributed ledger which records every transaction made in bitcoin and cannot be tampered with. Distributed ledger technology is something that banks feel can be used in different areas from identity checking to asset trading.

Blockchain (the company) announced on Tuesday that former Barclays CEO Anthony Jenkins was joining the board, in a move which is seen as validation for the technology. Smith said Jenkins will be key as Blockchain looks to scale its business.