"We had to cancel the show due to negative hype by people... it has everything to do with Jacaranda FM," the bar's marketing manager Gerhardt Theron told HuffPost SA.
Bester, who is also a singer, was due to perform at the bar on 29 September.
However, Theron explained that the decision to scrap the performance was made because of requests by punters who did not want Bester to perform.
"It's not us saying screw you Martin Bester, it's the people," he added.
Theron also explained that the bar neither supported or rejected what was said on the Jacaranda FM Breakfast Show by Bester's co-host Tumi Morake.
The pair co-host the show, on which Morake made the bicycle analogy which has angered some minority groups up such as AfriForum and Solidarity.
Others have said she was being perfectly accurate in what she said.
Last Tuesday, Morake said all race groups were just expected to unite after the demise of apartheid without any form of retribution. She then employed a bicycle analogy that was perceived to be offensive by many of the station's mostly white, Afrikaans-speaking listeners.
"It's like a child whose bicycle was taken forcefully away from him and then you say to the bully, 'no, no, no, share the bike together, don't be like that,'" Morake said.
Elephant Bull Sports Bar posted on Facebook that it would be cancelling the show.
Meanwhile many of Elephant Bull Sports Bar supporters have welcomed the decision to cancel Bester's show.
HuffPost SA was unable to get hold of Bester for comment.