Bitcoin prices have seen a strong rally this this week in the run-up to and following a U.S. Senate hearing on Monday, which has been interpreted favorably by traders, but the sheer size and speed of the rally has reignited fears of a bubble in the market. (Read More: Bitcoin hits $750, up 107% in a week)

On Tuesday, bitcoin prices touched a fresh record high of over $900 on the Mt. Gox exchange, a 6,445 percent increased on its value in January, when it traded at $13.75. However, it was a volatile morning that saw the currency plunge as low as $502. It was last trading around $625 by mid-morning U.S. time.

"Bitcoin does have some compelling things...that allow for it to be quite intriguing – but in terms of the price it's got way ahead of itself here in the short run," David McAlvany, CEO of McAlvany Financial Group told CNBC Asia's Squawk Box on Tuesday.

Meanwhile, Beat Wittmann, CEO of TCMG Asset Management, also told CNBC he would not be dabbling in the market: "I don't think (bitcoin will become a legitimate and regulated currency). It wouldn't be something I'll be playing," he added. (Read more: The Winklevosses: Bitcoin worth 100 times more)

Tweeters also joined the debate online Bitcoin is trading in a nearly $400 range today. Indecision in a rally is typically a reversal signal. This is not the first time that observers of bitcoin have called for a bubble, however. Back in April, when the price of the virtual currency surged 360 percent in the space of a month to trade around $141, Societe Generale analyst Sebastian Galy told CNBC that bitcoin was demonstrating bubble characteristics.

And last week, Peter Schiff, CEO of Euro Pacific Capital compared the recent excitement over bitcoin to the fantastic rise and fall of the value of tulip bulbs in 17th century Holland. He argued that there are no other positive drivers underlying the rally other than expectations of higher prices. (Read more: Bitcoin goes to Washington, and Brooklyn)

However, supporters of the currency strongly disagree and say bitcoin still has enormous upside. "There will be lots of ups and downs along the way, but bitcoin is the most important invention… since the internet," Roger Ver, director of business development at BitInstant, a service that provides fund transfers between and into bitcoin exchanges, told CNBC.

"As its use becomes widespread, each single bitcoin will need to be worth tens of thousands of U.S. dollars, or more, in order to accommodate the amount of trade that will be done with it," he added. (Read more: Could China make or break Bitcoin?)

Indeed, the use of the currency has exploded in recent times, and the total market is valued at around $7 billion, with around 12 million bitcoins in circulation. But bitcoin has faced stumbling blocks along the way and its reputation has been blighted with its association with criminal activity. Last month, the closure of Silk Road, the online marketplace that allegedly allowed more than a billion dollars of illegal drugs and illicit services to be bought using the virtual currency, helped boost bitcoin's perception as a credible currency alternative and has added strength to the rally.

According to Zennon Kapron, managing director of research firm Kapron Asia, bitcoin prices are in line for a correction but are not in bubble territory.

(Read more: Copycat Silk Road drug site reopens after FBI raid)