On Thursday, Bishop tweeted Poulter saying: "Faldo's record stands by itself. Six majors and all-time RC points. Yours vs. His? Lil Girl."
Bishop also took to Facebook to defend Faldo and Watson by mentioning their records as Major winners, before referring to Poulter by adding: "Really? Sounds like a little school girl squealing during recess. C'MON MAN!"
In response to the comments, Poulter told Golf Channel: "Is being called a 'lil girl' meant to be derogatory or a put down? That's pretty shocking and disappointing, especially coming from the leader of the PGA of America. No further comment."
Bishop has deleted the comments from his social media accounts.