To express that one is getting on a horse, a bicycle, a scooter and any form of transports that you don't get inside of, the correct preposition to use is "sur".
For example: "Il monte sur son cheval" (He gets on his horse).
However, when one is getting off a horse, bicycle, etc, you would still say "descendre de" as for a bus, a car, a train...
For example: "Elle va descendre de son vélo" (She's going to get off her bicycle)
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