>Might this have to do with horseriding? Don't you mount a horse from
>the right hand side?
not if you're a Sioux... My 2c: it is a convention. Right handed persons intuitivly do that, its like aiming a rifle at something: you automatically just hold it to your cheek, some people to the left one, others to he right one. And right-handedness was/is considered to be the norm, thus it influenced the way bicycles are built. There's millions of examples for this in daily life.
Martin Appel lefthanded guy from Munich, BY, Germany who would mount a horse as he mounts his bicycle: from the left side (if he could ride).