The CNN chat show host was sharing a flight with the 60-year-old star and revealed he was woken up repeatedly, eventually ''to the sight'' of her naked chest right in front of his face.
He told the Daily Mirror newspaper: ''We were incarcerated on a small plane for five hours flying to Los Angeles. I love Sharon but she was in a frisky mood after a coupe of glasses of red wine.
''I needed to sleep but every time I tried she'd wake me - shrieking and poking my nose or pulling my ears. I finally drifted off, only to get woken again.
''I opened my eyes to the sight of Sharon's naked right breast dangling two inches from my eyes.''
The 48-year-old star joked it was simply not the right time nor place to have the 'X Factor' UK judge's breast exposed to him.
He added: ''There is a time and a place for Sharon Osbourne's naked breast. But dangled in my face at 3am in the confines of a private jet really isn't it.''
The 55 year old actor joined Chris Martin and co. on stage in New Jersey to perform 'Earth Angel' and 'Johnny B. Goode'.
Bjork Digital comes to London's Somerset House in September, along with a single live show at the Royal Albert Hall.
There's very much a strength of conviction in remaining what you were, but arguably more so in becoming what you want to be.
The BBC drama starring Aidan Turner returns to BBC One on September 4th.