The coin fell sharply in May after a crackdown in China and a decision by Elon Musk’s Tesla not to accept it as payment any more.
But investor sentiment is improving as more mainstream financial companies begin using the digital currency.
Bitcoin is now up 81% since January, when it was trading at just $27,700.
On Monday, it climbed almost 3% to $50,266.90 while Ether, another popular digital coin, was up more than 4% at $3,367.51.
It came as PayPal said it would allow customers in the UK to buy, sell and hold Bitcoin and other digital currencies as it expands its crypto services outside of the US for the first time.
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With over 403 million active accounts globally, the US firm is one of the largest mainstream financial companies to offer users access to cryptocurrencies.
“This appears to be yet another example of a global company legitimising the use of crypto as it becomes more mainstream,” said Michael Hewson at CMC Markets.
Continued support from the US Federal Reserve for the US economy has also bolstered Bitcoin recently, analysts say. It is holding interest rates at record lows and making riskier assets more attractive to investors.
Neil Wison of Markets.com said Bitcoin’s rebound “shows no signs of cooling”, although he said he expected to see some “pullback” in the short term.
But Dan Ives from Wedbush Securities said Bitcoin remained “a highly volatile digital currency”, despite growing investor optimism.