Mr Arnold shared footage of police officers by the river lifting what appeared to be a body bag on his social media channels, in a video that has now been deleted.
He said on Sunday that “in hindsight, perhaps it was a little bit sensitive, perhaps it was bad timing to put that video online.
“I perhaps didn’t take into account the family at that time, I admit that.”
He said he had made a donation to the family “five times the amount that that particular video has made me”.
While Mr Arnold “won’t give figures away” regarding the total, he is alleged to have told The Sun it was likely to have made him £900 in royalties.
He said he had made the donation “out of respect”, adding: “I’d like to take this opportunity to apologise to the family for any upset caused by the videos”.
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Mr Arnold said the “whole point” of his channel was to help people and investigations “not to film bodies coming out of rivers”.
During the investigation, police criticised online sleuths spreading false information about the disappearance, saying rumours were “distracting” officers investigating the case.
Speaking at a news conference more than two weeks after Ms Bulley’s disappearance, Detective Superintendent Rebecca Smith said officers were being “inundated with false information, accusations and rumours” about Ms Bulley’s disappearance.
A YouTuber searching for Ms Bulley was handed a fixed penalty notice under section 4 of the Public Order Act: fear or provocation of violence.
Dan Duffy, 36, had posted clips to his 206,000 subscribers on YouTube saying he had “been in people’s back gardens at night-time”.