Did the Calgary Stampede ever feature buffalo riding?

No. To clarify the animal you are probably asking about is a bison, not a buffalo, though many people confuse the tow. (a buffalo is a smaller animal with curved horns. The animals that roamed the Alberta plains (and still do in smaller numbers) are bison.

Some types of Buffalo are domesticated (in Italy they make cheeses out of water buffalo milk) so it's possible some people have ridden them, but the animal that roamed the plains of Alberta (bison) is not domesticated and is far to dangerous to ride in any kind of event. They do raise bison in Alberta for meat.

It is liklely that the myth of people riding bison comes from this name confusion.

A bison also has a huge hump at its shoulders which would make riding it very difficult.