What is a good strategy for catching horses?
Method 1: Stealth
According to this guide, one strategy is to simply try to sneak up on the horses, and try to catch them in this way. If the horse is special in some way (eg the Giant Horse), using a meal or an elixir that temporarily helps improve stealth may help to capture the horse (eg see the Sneaky Elixir here). As you mentioned in your question apples can also be used to help woo horses, though some stealth may still be required.
You mentioned in your question this method can take a lot of time. I found this video showing how to use this method quickly - you'll note that the person actually fails catching a horse on his first try. This is OK, just keep trying and it will eventually work. Also try to approach from behind - this will ensure the horses don't notice you, and maximize your chances of catching one. You can also try using some armour that boosts your stealth.
Method 2: Bokoblins
Another method described here for catching a horse is to steal one from a mounted Bokoblin. While these horses may not have maximum bond with Link, they will be fairly easy to tame. Simply knock a Bokoblin off of its horse, and mount the horse to catch it.
Method 3: Paragliding
Finally, in my experience, you can also try to use your paraglider to drop on them from above. I found this to be a bit tricky to do (since you have to land perfectly on the horse), however if you are having problems with sneaking this method could work, since the horses tend not to notice when you're landing on them from above. Importantly, this method has one drawback: it robs you of your stamina, which you need to tame the horse. Since paragliding uses up stamina, and taming a horse also requires stamina, this method may not be feasible if you haven't already upgraded your stamina.
This video shows the general paragliding strategy, though as you can see, landing it correctly can be difficult.
I usually get them by sneaking up behind them and BARELY MOVING when I am crouched. Also, stealth dishes or clothes could help.