Ninety taxi operators from Mitchells Plain and Khayelitsha are completing business development modul.
The 22-year-old Richards Bay woman was cycling with a group of friends on Saturday when the crash occurred.
The latest accident comes as KwaZulu-Natal Cycling president Greg Stedman slammed impatient motorists and their lack of respect for the laws of the road.
Calling on cyclists to lead by example in the use of roads, Stedman said: "It is a difficult problem ... It is caused by intolerance.
"South Africans need to realise that we have a problem ... compounded by the lack of strict policing, impatience and a lack of respect for the law."
He said all South Africans needed to determine what could be done to avoid such accidents.
"Together with Cycling SA, we will sit down and think of ways to address this problem."
Netcare 911 spokesman Chris Botha said the woman was riding in a group when a motorist crashed his car into her before hitting a lamp post.
"The critically injured cyclist was stabilised before she was taken to hospital. A passenger in the car was injured and taken to a provincial hospital for treatment," Botha said.
The motorist was taken in for questioning by police officers.
Meanwhile, KwaZulu-Natal police investigating Stander's death said the taxi driver had cooperated with them.
Police spokesman Colonel Jay Naicker said the driver would be charged with culpable homicide and appear in the Port Shepstone Magistrate's Court today.
Stander died after he was hit by a taxi in Shelly Beach on the KwaZulu- Natal South Coast while on a training ride on Thursday afternoon.
Memorial rides took place across the country over the weekend to commemorate Stander's life.