The former boxer angered the rest of base camp when he complained that Washington had cooked the chicken incorrectly and should have stuck to washing up.
The next morning, Washington said that she felt under too much "pressure" to cook, while Justin Ryan, who had defended her, said that he had "babbled with rage".
However, speaking in the Bush Telegraph, Bugner explained that he regrets his comments, saying: "I personally may have lost it yesterday for whatever reason and I regret it now because realistically we've all got to stick together."
He also apologised to the group, telling them: "It was nothing to do with the food, it's nothing to do with anyone. I thought, 'I hope they throw me off now - I'm ready to go'."
Ryan replied: "I can't forget what you said, but I'm prepared to draw a line under it and have a compliant and happy camp. But the content of your delivery and argument yesterday left my stomach turning, Joe. You said some despicable, reprehensible stuff."
Bugner later praised the group's evening meal, describing it as "beautiful".