The trio were seen performing on last weekend's auditions episode of the ITV1 show but failed to make it through to Boot Camp.
At Guildford's Scrumptious nightclub on Sunday, the singers were allegedly called "n***ers" by the venue's drag queen compere as he was introducing them to the crowd.
Band member Pinky told The Sun: "Just before we came out on stage the drag queen said, 'We've got some n***ers backstage!' He used the term three times in total."
It is claimed that once the transvestite had realised that Bun 'nd Cheese and their family had heard the slur, he apologised but used the word again.
Pinky added: "When we came on stage he said, 'I apologise for calling you n***ers'. [My bandmates] Patty and Peas were very upset. Patty was very angry. It was just appalling.
"It's the first time in my life I've been called that and it hurt. There were about 100 people in the audience. The truth is that we were the only black people there and no-one seemed to care what we'd been called."