Branson met Clark last week after the inaugural fight of his Virgin Atlantic airline from London to Vancouver.
Later, he issued an invitation on his blog that included a photo of a naked model riding on his back while kitesurfing.
Clark said she found the offer disrespectful, and Branson has taken to Twitter to issue an apology, saying the invitation was a joke and no offence was meant.
Clark said this is a case of a lighthearted joke backfiring, but she accepts the apology.
"Lighthearted jokes often have a place, but I don't think that this was appropriate," she said. "Of course, I accept his apology."
She originally turned down the kitesurfing offer with a joke of her own, saying if the invitation is Branson's best pick-up line, there may be a reason the name of his company Virgin.