Possibly not all sky bison were domesticated. There were likely wild herds of bison living in the mountains or out roaming the wilderness. The bison at the Air Temples were all destroyed save Appa.

However Firelord Sozin lacked the manpower to track and destroy every last flying bison or he may have been unaware other bison existed. So the wild herds were safe.

Aang encountered a surviving herd on an island during his travels and brought them to the Air Temple. He discovered a new breed of bison with brown ears not white.

This flying bison is named Oogi and its a descendant of the herd. Numerous other bison live on the island. Healthy colonies of flying bison also live at the Air Temples where the acolytes look after them and other bison live in the wilderness around the temples.

I never thought this bison was Appa. The Avatar has a strong spiritual bond with their animal guide and the guide normally dies alongside or soon after the Avatar.

Avatar Roku had a dragon called Fang that chose to die at his side in the volcanic eruption. I reckon Appa would die with Aang or soon after him.