Good question and that can only be answered by the Bing Engineers that developed the search engine ranking algorithm. I'd say that Bing and Google both give some like to FB likes but neither use it overly.
FB Likes are mainly to spread word around Facebook as a viral type effect.
Just say they do consider Facebook likes more relevant and try to get as many as you can. However, be sure to diversify by getting others to post about your site on their Facebook wall/Twitter/Google + profile. All these backlinks help
But won't Bing get wise to how webmasters are paying people to like their Facebook page? So those people don't really LIKE the page they're just clicking a button over incentive. That's no real indicator of the page's worth. I hope there are counter balancing factors.