The singer told Geoff Lloyd on Absolute Radio that his group met the actress in The Viper Room nightclub in Los Angeles over two decades ago.
Ryder said: "It was when Julia had just released Pretty Woman and we was in the Viper, and she took a liking to Bez.
"Really, she invited him home, but Bez actually got on more with Evil, her bodyguard. Bez was just... Evil was just so cool... He didn't know who Julia Roberts was."
Bez won the third series of Celebrity Big Brother in 2005, but was declared bankrupt for a second time three years later.
It was claimed last December that Bez, whose real name is Mark Berry, had been involved in an organised bare-knuckle fight over his ex-partner.
Of accidentally turning up on stage at a Simply Red show, Ryder explained: "I'm late for the gig and I see a big queue outside one of the Apollo venues.
"We'd think, 'That's where we're playing', so just bust in the gaff, go right down the auditorium and jump on the stage and get up."
He added: "That's when I've seen saxophones and hats and things that didn't fit with us. Then I saw Mick [Hucknall]'s head peering round from the dressing room and realised that we was in the wrong venue. We was actually at the Polytechnic just over the road."
Watch the Shaun Ryder and Russell Watson 'Barcelona' music video below: