He was later taken from the rodeo ring by ambulance to a nearby car park, where he was picked up by helicopter and taken to Dunedin Hospital.
St John spokesman Ian Henderson said Mr Billing suffered "serious injuries, including possible spinal injuries".
He was still being assessed in the emergency department last night.
Mr Doherty said the injured cowboy was an experienced rider, who had returned this season after a break.
"It is one of those things that happen. A rodeo is inherently dangerous, I guess, and we don't like to see things like that happen, but occasionally it does."
Earlier in the open saddle bronc competition, judge Johnny Robinson, of Lawrence, sustained a minor leg injury after being hit by a horse that had just bucked off its rider.
The annual Outram Rodeo attracted several thousand spectators and "from a club's point of view we are happy with how things went, but we didn't like to see those couple of injuries".