Bishop was relieved of his duties last week, after branding Ian Poulter a "Lil Girl" on Twitter in response to the English golfer criticising Nick Faldo's stint as Europe's Ryder Cup captain.
The PGA of America labelled the incident "unacceptable" and made reference to "insensitive gender-based statements" when confirming the dismissal of Bishop, who also directed a similar comment towards Poulter on Facebook.
However, in a lengthy interview with Golf World, Bishop - a friend of Faldo upset by criticism of the six-time major winner and US Ryder Cup captain Tom Watson - expressed disappointment at the chain of events that followed his initial messages to Poulter.
Recalling his immediate reaction, Bishop said: "To be honest with you, there was no hesitation when I typed 'Lil Girl', because I kind of grew up in a generation where when my dad hit ground balls to me in the back yard, if I pulled my head up, he told me I was fielding like a girl.
"But in that restroom at The Greenbrier [resort, where he viewed tweets labelling him a sexist], the light went on, and I thought, 'Oh my God, I didn't even think about that. How stupid could I be?'
"I felt like throwing up. I was for inclusion of women in the R&A and for their equality in the game. I'm not a sexist."
Bishop claims he was advised by the PGA not to do any interviews as the furore escalated, with the organisation instead releasing a statement on his behalf that he felt showed "no remorse whatsoever".
"My biggest regret in all this is not getting my own apology out," he added. "I've gotten killed from some people saying that I never apologised, or I waited too long to apologise, but that was totally out of my control."
Detailing the comments he made in a subsequent teleconference called by the PGA board, Bishop added: "I apologised to the board, reiterated that I had very much wanted to make a public apology. And I said I don't think the punishment fits the crime.
"And that doesn't mean I don't have remorse for what I did. Trust me, I abused my platform. I know I made a huge mistake. I'm the first to say that.
"I let my personal feelings for two guys [Faldo and Watson] get in my way, and used a bad choice of words in trying to convey my frustration.
"I think the PGA of America needs to be in position to explain why this thing came down as it did. I don't think it was totally fair."