"I have a donkey but I am riding a horse."
Translation:Eşeğim var ama ata biniyorum.
I am having a real hard time remembering 'binmek' gets dative, not accusative case.
It is actually more of a translation of "getting on" rather than "riding". A more accurate word for ride is "sürmek", which is accusative; but it is only used for vehicles (at least in its primary sense).
Now that I think, it's odd that there isn't a perfect/specific translation for riding an animal in Turkish, despite the high utilization of horses in Turkic history. Perhaps the old Turks were so used to horses that they felt getting on a horse was little different from riding it.