Members of the WBCS were among the 150 people present during the act which took place during a party thrown by businessman Enzo Sauro to celebrate the signing of a deal between his company Cig Calon Cymru Cyf and Marks & Spencer.
The society is said to be "up-in-arms" over the incident. Sauro, whose business, which specialises in pedigree Welsh Black beef, based in Cross Hands, Llanelli, said he had no idea the woman would strip and claimed the incident had nothing to do with him. Most members of the WBCS, whose patron is Prince Charles, have written to complain.
An inquiry has now been launched into the incident at the show which was held in Bulith Wells, Powys last week.
President of the WBCS, Bob Williams, told MTJ that he could not confirm whether Sauro was in any way connected to the incident, but if it emerged that he was, then it would be an extra blow to the society, because he was not only a member but also sat on its council. He added: "The WBCS had absolutely nothing, and I emphasise that, to do with this incident. We are very upset and very concerned about it.
"We were going to hold a special meeting about it with Mr Sauro because we wanted to clear up the matter but he is going to be away and so is our chief executive, so we won't be doing anything about it until he returns to work. Whether we take any action or not remains to be seen."
He alleged that the woman involved was an employee of Sauro's company and said Sauro should have intervened and stopped her. "As president of the WBCS I have been very upset about the matter. It's an unsavoury matter that we would like to forget as soon as we can," Williams said.
Sauro was unavailable for comment, however, in a national newspaper report he said: "I am absolutely numb. A young girl danced on a table. I didn't force her to dance on the table and certainly did not organise it. It just happened. If that's what she decides to do in her social hours that's up to her."
Builder-turned-farmer Sauro is one of the country's most prominent breeders of Welsh Black Cattle.The contract he was celebrating is to supply beef from 15 to 20 Welsh Black cattle a week for M&S's 16 stores in Wales.