Back in 2007, when Bing was named Live Search, Microsoft introduced their flavor of Google PageRank and cleverly named it "Page Score." If you verify your site with Bing Webmaster Tools at bing.com/webmaster, you should be able to see your Page Score value, X out of 5 green bars.
This site has 5 green bars for the domain and our top five pages:
But what does "Page Score" actually mean? A Bing Forum thread asked that question and a Bing representative replies saying:
It is a rough indication of how we view your site pages. Note that this score is only relevent to your site and does not track well in our index.
I looked up what the help section of webmaster tools says and it explains page score as:
Provides a measurement of how authoritative Bing views your webpage to be, with five green boxes being the highest rating and five empty boxes being the lowest. This is based on many of the same factors Bing uses to determine static rank, but isn't directly comparable.
Forum discussion at Bing Forum.