The bishop also said he was planning to be out of the country on a "republican day trip to France" the day the couple weds, which may be declared a national holiday.
"I accept that this was a major error of judgment on my part," Broadbent said. "I recognize that the tone of my language and the content of what I said were deeply offensive, and I apologize unreservedly for the hurt caused."
The bishop added that "it was unwise of me to engage in a debate with others on a semi-public Internet forum and to express myself in such language."
Prince Charles and his representative declined to comment on the bishop's apology or the earlier comments.
Broadbent also said he wishes the couple well.
"I wish Prince William and Kate Middleton a happy and lifelong marriage, and will hold them in my prayers," he said.
The royal family has yet to announce the date and the location of the wedding.