The late princess - who died in a Paris car accident in 1997 - sat next to the 71-year-old actor at the 1989 royal premiere in London and they quietly joked with one another between the scenes.
Billy said: ''The lights went down and she whispered to me, 'I'm taking my shoes off.' So I went, 'I'm taking my pants off.' And she goes, 'Oh, you're so naughty!' ''
On the other side of Diana was director Rob Reiner, and he was particularly worried about the princess' reaction to Sally Albright (Meg Ryan)'s infamous orgasm scene.
He recalled to People magazine: ''All I'm thinking the entire time is, 'How is she responding to this?'
''And now the orgasm scene is coming, I'm going 'Oh God. Oh my God.'
But Billy and Rob weren't the only people thinking about Diana's reaction to the scene.
The director said: ''''She turned to Billy and says, 'I'd be laughing a lot more, except I know everybody's looking at me.'
Billy added: ''People in the audience knew when [the scene] was happening, they all started to shift their weight to see how she was going to react. It was crazy fun.''
The 'City Slickers' actor particularly remembered the princess' ''terrible laugh''.
He said: ''She had this terrible laugh! And I said to Rob later, 'If this was a date, I'd never see her again! Just because she laughs like ''Eh heh eh heh.'' ' ''
Despite the pair's worries, it seems Diana had a great time at the premiere.
Rob said: ''She asked for the film at Buckingham Palace so she could watch it with her friends.''
American Thighs was released on this day in 1994.