Depends what you call a professional. When I look at my old trainer, he started riding and jumping ponies at 6 years old, he is now 21 years old and rides 2**-3*** shows and rides for an Olympic rider.
Expert? No such thing. Everyday everyone is learning. Learning new things about their horse or a new trick to learn with their riding style. But to get experience within jumping normally a couple of years
totally dependent on the individual
It all depends on your trainer, how many lessons you get a week/month, the horse you're riding, your confidence and your skill. It's hard to say exactly how long.
You can learn how to jump in a year or two but in jumping it's more that experience matters. And the longest you do it the better you become.
People that are one of the bests and are winning the biggest competitionns have been practicing for over ten or twenty years and even more on different kind of horses in different environments and had a lot of falls before they became masters.