While filming Friday night's show at Television Centre in west London, Ross promised to be "more aware" in future.
Sky News reporter Enda Brady was among the 300-strong audience. He said that Ross, wearing a red suit and white shirt, began the performance with a series of jokes about outgoing US president George Bush.
He then said: "What kind of idiot would say stuff like that, knowing it would be broadcast? Seriously, I would like to apologise. We have got a great responsibility, what we do is a privilege and I will be more aware in future."
Ross's wife Jane arrived at the studios to support her husband. A long queue of audience members snaked around part of the BBC building as they waited to get in.
Tom Cruise, one of the guests on the show, arrived in a blacked-out car without commenting to reporters.
Brady said Ross's first words to the audience as he walked out to noisy applause were: "So, where were we?"
Ross said someone had sent him a gargoyle with his face and joked that he looked up the definition of gargoyle in the dictionary to find it described as: "Something that spills filth into the gutter."
Brady said that when Lee Evans, one of the guests on the show, used a swearword, Ross kicked him off, saying they were in a "brave new age".