The coin has seen its value double in the last month in a volatile journey.
Its latest milestone came after Bitcoin surged by another $1,000 in value in less than 24 hours.
Spread betting firm CMC Markets said the rise had all the symptoms of a bubble market, warning "there is no way to know when the bubble will burst".
The digital currency's rapid ascent from $1,000 at the start of the year has put it in the spotlight.
Critics have said Bitcoin is going through a bubble similar to the dotcom boom, whereas others say it is rising in price because it is crossing into the financial mainstream.
But Leonhard Weese, president of the Bitcoin Association of Hong Kong, said the rise in Bitcoin's value was "mostly motivated by fear of missing out and greed".
Bitcoins are created through a complex computer process known as mining, and then monitored by a network of computers across the world.
A steady stream of about 3,600 new bitcoins are created a day - with about 16.5 million now in circulation from a maximum limit of 21 million.