Though Bishop later removed his own comments from Twitter and Facebook and said that he "could have selected some different ways" to express his opinion, his statements were deemed to be inconsistent with the policies of the PGA.
"The PGA of America understands the enormous responsibility it has to lead this great game and to enrich lives in our society through golf," chief executive officer Pete Bevacqua said in a statement.
"We must demand of ourselves that we make golf both welcoming and inclusive to all who want to experience it, and everyone at the PGA of America must lead by example."
PGA of America vice president Derek Sprague has been appointed as interim president until Nov. 22, when the election of new national officers will take place at the PGA's 98th annual meeting.
"The members and apprentices of the PGA of America must uphold the highest standards and values of the profession, as well as the manner in which we conduct ourselves at all times," said Sprague.
"We apologise to any individual or group that felt diminished, in any way, by this unacceptable incident."
Bishop later released a statement after he was sacked from the organisation, which represents more than 27,000 golf professionals, runs the year's final major, the PGA Championship, and also the Ryder Cup when it is staged in the United States.
"I want to apologise to Ian Poulter and anyone else that I might have offended ... particularly, I have great remorse that my comments contained the words 'little girl' because I have always been a great advocate for girls and women in golf," the statement said.
"This is a classic example of poor use of social media on my part and if I had the chance to hit the delete button on the things that I sent out yesterday, I would without hesitation."
Poulter, writing in his autobiography "No Limits", said the 2014 European Ryder Cup team were furious with Faldo who was captain during the 2008 defeat in Kentucky.
RESPECT LOST
According to Poulter, Faldo had lost the respect of Europe's top players after he described Spaniard Sergio Garcia as "useless" during their Ryder Cup victory over the United States at Gleneagles in Scotland this month.
"It makes me laugh," Poulter wrote. "Faldo is talking about someone being useless at the 2008 Ryder Cup. That's the Ryder Cup where he was captain. That's the Ryder Cup where the Europe team suffered a heavy defeat.
"So who's useless? Faldo might need to have a little look in the mirror."
Bishop, who owns a large golf complex in Indiana and had just one month left on his two-year term as PGA president, tweeted to Poulter: "Faldo's record stands by itself. Six majors and all-time RC (Ryder Cup) points. Yours vs. His? Lil Girl."
And on Facebook, he said: "Tom Watson (8 majors and a 10-3-1 Ryder Cup record) and Nick Faldo (6 majors and all-time Ryder Cup points leader) get bashed by Ian James Poulter. Really? Sounds like a little school girl squealing during recess. C'MON MAN!"
In response, 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."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Gene Cherry)
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