The 28-year-old royal and Bonas, 24, made headlines this week when they were photographed hugging and kissing during a Swiss ski getaway.
The Sun said Harry will be Bonas' date to Isabella Anstruther-Gough-Calthorpe's upcoming wedding to Richard Branson's businessman son, Sam.
Harry is also a friend of the groom and Bonas has been friends with Harry's cousins, Princesses Beatrice and Eugenie, for years.
"Harry and Cressie are at the exciting stage of a relationship where they just want to spend as much time together as possible," an insider told the newspaper. "He has ties to the Branson family, so everyone's incredibly excited at the prospect of seeing them together in South Africa."