"The Flight of Dragons," by Peter Dickinson proposed a plausible evolutionary explanation of dragons. Plausible to my 13yo mind, at least. In it, he explained that dragon flight is a hybrid of wing based propulsion and lighter than air flight. The buoyancy was provided for by hydrogen, which also accounted for fire breath (ignited by an electric spark). The hydrogen was created through a chemical process involving acid, which accounted for dragon hoards as everything but gold would be corroded by dragon spit. I remember it being a pretty cohesive account.
Evolutionarily, I don't think this would be much more of a stretch than what we see on earth today. We have flying animals. We have animals that puff themselves up to ward off threats. We have serpents with amazingly elastic bodies. We have animals that produce acid. We have electric eels. I think if you work out something physically plausible the evolutionary explanation will be as good as any we have for existing animals.
Edit: And as for the mount aspect. It's been mentioned that birds will carry off small mammals, so there is always that. There could be explanations on the sexual selection side. Perhaps (this might have been in Flight of Dragons) flight and fire displays could have been involved in courtship. Females prefer males which could stay afloat longer with more of their hydrogen being burned, implying quick generation of gas or super buoyancy. Courtship could involve the males trying to lift the females and the females trying to escape downward.