I doubt it. Almost no one expects Bing to make much headway against Google.
For one thing, many of us don't trust Microft not to artificially influence results to steer toward their own properties or to bury anti-Microsoft results. I would hope they'd know better, but their history of immorality makes them suspect.
Of course Google could be equally dishonest, but so far they have not, while some say Microsoft did salt results the last time they floated a search engine.
That charge could be completely false- I saw lousy results, but never anything I thought was duplicitous, so those who insist that may have confused incompetence with chicanery, but regardless, the taint is there.