
The reason riding a horse is like riding a bike is because of muscle memories or muscle reflex to be more accurate, rather than going up to the CNS this reflex is formed in the spinal cord itself making it work faster and also the reason we don't require much thinking (it happens with the help of repeated practice which the cerebrum and cerebellum than translates into a muscle reflex but I guess it's all unnecessary details). Well basically for her to be able to ride instinctly, she needs her old body which had gone through that practice and not exactly her memories, heck her older body could most probably ride without any memories just fine but not vice versa. What could actually explain this situation would be that while she was in her father's house her education had already started so she basically knew how to ride regardless of the age of her body and it just wasn't shown, after all nobody shows much surprise to even the 8th prince riding so I guess the riding practices are still ongoing, just not shown.
The way how the FL started riding the horse so professionally in just one go (or the way we were shown) it's just so unreal. She learnt all of these tricks in her past life but in this life her body is not used to these tricks. How the heck will she pull it off so flawlessly? That's impossible.