The only time I left the saddle unintentionally involved a muddy, slippery hillside and a horse that fell/rolled.
I’ve had deer pop up right in front of me, grouse, pheasant, turkey flushing, etc. Always managed to stay in my saddle.
Then again I knew someone who was partially thrown but had a foot caught in the stirrup. The horse bolted. They died from head trauma.
Just want to do basic trail riding with western style saddle. Nothing fancy.
With normal aptitude and a cooperative horse, you can learn enough to do this - and enjoy it - in a couple of hours.
A short vacation on a Western dude ranch would be ideal. Their horses are well trained and the staff/cow hands are accustomed to instructing tourists.
I think they’d take someone on guided trails the first day.
That would be a good start. The rest is gaining experience with different horses and learning how to do it comfortably without bouncing. I never quite learned that skill. 
My bottom got sore.
If that’s what you want to do, spend some time at a place that offers trail rides. They’ll show you the ropes and will have horses or mules that are just your speed (so to speak). You shouldn’t need lessons to do this.
I suspect that instructor was talking about the difference between riding and Riding. Also the difference between money in your wallet and money in hers…
When our daughter Elizabeth was seven years old we took her horseback riding for the first time. It was a place we found while on vacation in SW Ohio. It was nice, slow, leisurely ride through the woods, led by someone who worked there. It lasted about 45 minutes.
Afterwards I said to her, “You did pretty good. Hey, maybe you should take horse riding lessons!”
She replied, in a somewhat serious tone, “Why? I already know how to ride a horse.”
My daughter went from: “I want to ride, I want to ride” to “The horse is too big”.
caveat – if you want to head out on your own, there should be someone in the group who knows a lot about horses and riding. And if that’s not you, and you want to head out alone, you should take some classes, or at least log a lot of experience.
But yeah, if you want to go with a friend who rides, or are happy to go in a group, you don’t need any lessons. Well, the very first time, someone will have to tell you how to mount, how to dismount, and how to tell the horse you want it to “go/stop/turn”. But that shouldn’t take very long.
When I was a kid, a friend of the family came out to visit with their kid. My brother, sister, and the visiting kid went trail riding. We only had three horses, so I stayed home with the adults.
We were all sitting in the kitchen when a big shadow blocked sunlight from a kitchen window. Outside there were three horses, sans riders.
I helped unsaddle the horses then about 30 minutes later the three lost riders came limping home.
Although I did some casual riding as a teenager, I took some lessons as an adult that took me beyond simple trail riding. I’d say it took about ten lessons to get to the point where I could predictably get the horse to trot, canter and gallop and feel comfortable riding.
I often wondered about actors and horse riding and how long it took a green horn to get it down. Some seem to be pretty competent at riding fast. Yes, some are stunt doubles but many are not.
Some actors spend a lot of time learning to ride before the movie films, and some actors are really bad at it if you know what you’re looking at.
Likely a long time before I go out on my own.
I stayed a week plus at a horse ranch outside of Yellowstone when I was 9. Before I was 12 I had been to two week-long horse ranch summer camps. (The second one still classed me as a “Desperado,” i.e. beginner, because I hadn’t been to their camp before. 
) I don’t really remember when I didn’t know how to ride a horse. In my mind it’s brain-dead simple.
But then I think of how it would be as an adult starting from scratch, especially a person who doesn’t have that animal husbandry trait. If you’re going for simple trail rides, it shouldn’t take more than a few days. If you want to look like you grew up in the saddle, or do rodeo, dressage, or actual cowboy shit, you’ll need months.
My goal is to learn all the basics by Halloween or Thanksgiving. Depends on how many lessons I can get in. They say I should do 2 per week and I will probably do that most weeks.
There’s a difference between being able to stay on a horse in motion, and riding.
Balance and body awareness are key, flexibility and strength (whole body, not arm!) factor in too. I spent over 20 years teaching people of all ages to ride, and some picked it up really easily, some had to really work at it, some were hooked, and some just didn’t care about it much. The ones who had an easy time of it were not necessarily the ones that loved it, and those categories covered all ages. I’ve taught 3 yo beginners and 83 yo beginners.
One of the hardest things is your own balance. The stirrups on the saddle and the reins in your hands are NOT to keep you on the horse. The saddle is for comfort - you and the horse. The stirrups can be a help, but they are mostly for the rider’s comfort. They don’t provide a lot of stability though, they’re essentially a strap hanging from a single pivot point. Western saddles swing less than English, but it’s still not like feet-on-the-floor stability.
Communication with the horse is via the reins in your hands, your legs, and your body weight + position (your “seat”). The reins will not keep you on the horse, and mishandled reins can cause the horse pain. A horse in pain is not likely to be cooperative for long. At a very basic level the reins are used to signal turns and stopping. In more finessed riding, the reins are only a small part of the conversation, and the speed and direction are mostly influenced by the rider’s seat and legs.
I mentioned body awareness above. One of the real needs in riding is to be able to use one part of your body without it affecting another part. In can get very, very nuanced, but in broad terms you need to think of splitting yourself in 4 + chunks:
Upper (waist up, sometimes including your head but not always)
Lower (waist down)
Left (shoulder to heel)
right (shoulder to heel )
Head & eyes
As an example, if you need to make a tight right turn, maybe threading between trees, you’d need to use your head/eyes to look at the path you want to take, use a bit of right rein to cue the direction, softly close your left leg on the horse’s side to stop any drift that direction.
In a more beginner-centric example, you need to be able to keep your upper body from influencing your leg position. When humans get tense on a horse, we curl up and ‘go fetal’. That motion tends to make the legs swing up and back towards the horse’s butt, and that is when it’s easiest to fall off. To be solid in the saddle you need an upright position, with legs long and softly straight underneath you. Sometimes you do need to lean forward, but it has to be done still keeping your legs long.
Rein grip is a another hard thing, starting out. Humans control their world with hands, and when things get a bit scary we want to grab, clutch, pull. You can’t do that with reins, it won’t keep you on (and it will hurt/piss off the horse). They are attached to the horse’s mouth, which is at the end of a long and muscular neck - ie: no stability there.
The staying on part of riding needs soft strength, the real riding part of riding needs the ability to control your own body enough to influence theirs. If you can balance well on one leg, (and equally well on the left or the right), can sit on a balance ball or the edge of a rocking chair with your feet off the floor, you should have a relatively easy time learning to sit a horse, and then you can learn to ride.
Be careful, it’s addicting!
(I’m mostly an English rider, Western is a little different at the basic level, but not a lot. As you go up the levels and branch out into different disciplines within horse sports things get a good deal more varied!)
@saje, excellent response!
Riding is one of those things that is more of an art than a skill set. It would be like asking, how long before I can play classical guitar?
Thinking with the horse is not something that can be readily taught, but if it is not present, you’ll be a crap rider forever, and your riding will always be mechanical. The real joy of riding is when you and your horse are like tango dancers, a wordless continual flowing conversation between two minds and bodies. This can be very casual (‘I think this is a nice place for a trot’) to exact (negotiating opening and closing a gate from horseback, or choosing the right stride length for the best jump takeoff).
A more prosaic but equally vital piece is what you might call “the right automatic response”. When a horse stumbles, 'throwing him the reins" so he has the freedom of his neck and head to recover with. They aren’t handles! Or when a horse spooks and jumps, spinning him to face what he was frightened by (otherwise a startle might turn into a mad flight).
I never “curl and freeze” when my horse does something unexpected. That reflex has been erased in me. I do something – automatically – to recover my own and my horse’s stability. That is a product of my fearless foolhardy youth in the saddle. This appears to be quite difficult to acquire for most beginner adults, from what I’ve seen.
I use to ride my sister’s horse quite a bit when I was in high school. I would ride the horse to a nearby creek and let him play in the water, he loved it. After not riding for years, an ex girlfriend and I rented a couple horses at the beach for an hour. Got the 5 minute riding lesson and the stick with the orange flag. If the horse pooped, we were suppose to stop and mark it with the flag so the owner could pick it up. We enjoyed our horse ride. The next morning we could hardly walk, our butt muscles were very sore.
Broken toe so I will take 2 weeks off from lessons.
Compare it to learning to drive stick shift. An hour to learn the basics and get on the road/trail. 15-20 for it to feel natural and start learning some advanced techniques (trot, canter, gallop, double shift). 100’s to master.