The impressionist regularly targeted the Amstrad tycoon on his comedy show Dead Ringers after Sugar's reality series The Apprentice launched in 2005.
In one episode, Culshaw referred to Sugar as "Britain's most successful hedgehog". He also mocked Amstrad, describing it as "the Lego version of Microsoft".
Speaking about the BAFTA meeting in an interview with the Daily Record, Culshaw revealed: "My girlfriend at the time was saying that he was staring at me and pointing. She then said: 'He is walking over'. I kind of panicked.
"I thought he wasn't going to take what I had been doing very well. I'm about to be chastised and the BAFTAs is going to turn into a boardroom.
"He did the 'You're Fired' finger point but it turned into a wave. He came over and said: 'Very nice to meet you at last. We watch the show and we love it. You do it best, I have to say. I didn't realise I had all these little movements'."
The Apprentice returned for a new series on BBC One on Wednesday night.