You must rein in a wild horse.
You must rein a wild horse.
Can you ride on a horse?
Can you ride a horse?

The first two sentences are hard to assess without more information about their context/intent. For example, are they supposed to be explaining a general truth? Giving someone tips on how to ride? Something else?

When asking about someone’s ability to sit on a horse and control it, the correct form is “Can you ride a horse?”

“Can you ride on a horse?” is less usual and seems to be asking about the general possibility of people taming and riding horses.

He is riding a horse.
He is riding on a horse.
Ann rides in the bus to work.(BE)
Ann rides the bus to work. (AE)
All are possible sentences?

“He is riding a horse” is the more common form. “He is riding on a horse” is also possible, and makes the activity sound more important, or more of an “occasion”.

“Ann rides in the bus to work” is not natural to me. If I used a preposition it would be “on”.

Should I say ?: I ride a bicycle or I ride on a bicycle.

Normally you would say “I ride a bicycle”.