The Welsh forward, who will be back in the Premier League next season after claiming the Championship title with Cardiff City, spoke with the Toffees while looking for a route out of Newcastle United.
An agreement on personal terms was reached and Bellamy was convinced that he would be heading for Goodison Park.
No deal was to be pushed through, though, and Bellamy ended up heading elsewhere.
He says a meeting with Moyes, who is set to leave Everton this summer for Manchester United, scuppered a move by presenting him with a 'bizarre' list of rules which included not shaking his head if given an instruction during a game and speaking directly to the manager, and no-one else, if he had anything on his mind.
In his autobiography, serialised in the Daily Mirror, Bellamy wrote: "I would have signed without that second meeting, but now I couldn't.
"I don't hold a grudge and have got a lot of time for him. My guess is someone told him I would be trouble, and he panicked."