"You're very sexy in person by the way," "The Last Hurrah" singer blurted out. "You have, like, seven kids... but I'm just saying."
A flustered Costner responded, "I have all the stuff...".
Bebe later revealed that "The Bodyguard" - Costner's film with Whitney Houston - was one of her favourites.
The compliment would have helped the movie star score a few points at home with his wife, Christine Baumgartner - he recently told Press Association, "I try to take care of myself. I have a beautiful wife and I don’t want her to look anywhere else. I want to be something for her. I want to stay interested in life."