The paper published photos of the pair openly embracing on the snow-capped mountains of the Swiss Alps while vacationing at a ski resort in Verbier, Switzerland.
Bonas, 24, and Harry were first spotted together at the London premiere of "The Dark Knight Rises" in July and reportedly partied together at the Necker Island estate of Virgin mogul Sir Richard Branson just before Harry's infamous trip to Las Vegas in August
"She's an extremely fun girl but she's quite a wild thing too, and would have a nightmare if she was dating Harry," a source said of Bonas to the Daily Mirror in July.
Bonas, the daughter of 1960s model Lady Mark-Gaye Georgiana Lorna Curzon, was reportedly introduced to her prince by his cousin, Princess Eugenie, the daughter of Sarah Ferguson, Duchess of York, and Prince Andrew.
They are reportedly in Switzerland with the royal family, including second daughter, Beatrice, to celebrate Prince Andrew's 53rd birthday.
"It was clear they couldn't keep their hands off each other," one eyewitness told U.K.'s The Sun. "One minute they sat at the table with Andrew, Fergie and their daughters, the next they were acting like teenagers in a darkened cinema."
Harry just returned from a tour of duty in Afghanistan as a pilot for the British Army, where he is known as "Captain Wales." In a series of interviews given upon his return, the prince indicated he would not be immediately following the route of his older brother, Prince William, expecting a royal heir with wife Kate Middleton.
"I don't think you can ever be urged to settle down," Harry said. "If you find the right person and everything's right, it takes time, for myself and my brother."
Prior to the new photos, it was reported that Harry's relationship with Bonas had cooled because of his time away in Afghanistan and her tiring of the circus that surrounded Harry in England.
"I think Harry is not afraid to tell us now that this is a girl who he's not afraid of making a commitment to," Victoria Murphy, royal reporter for the U.K.'s Daily Mirror, told ABC News of the seemingly invigorated relationship.
Harry brought longtime girlfriend Chelsea Davy to Kate and William's wedding in April 2011, but that romance fizzled after nearly seven years when Davy reportedly couldn't stand the limelight and paparazzi pressure that came with Harry's royal title.
In April, reports stated that Harry was "smitten" with Mollie King, 24, a member of the all-girl pop group The Saturdays, after the pair was spotted by British paparazzi singing karaoke with friends at London's Bunga Bunga club.