Yeah, see, I don't really use/need continuous or burst mode anymore because I know exactly when to press the shutter to get the right stride, and I save myself a ton of space and time that way.
I actually don't know of any horse photography books... I've never read any, just grew up immersed in horses and the horse world and got into show Arabs as an adult, so I saw the photos in the horse magazines I devoured and the ones my trainers featured on their website etc etc. I've seen ONE or two on amazon but can't vouch for them since they are likely pretty general, and the horse world is very specialized.
The tricky thing is that a lot of what is wanted in a photo differs A LOT by breed - for instance, at the trot, Arabs want a shot with the base of the neck held high and the neck itself hooked, the tail flagged in the air, and showing as much knee action as possible, so you press the shutter right as the horse lifts its inside leg to get the 'look' of the most knee action as possible, vs quarter horse people want a shot where the horse's frame is long and low (head down), the tail FLAT against the buttocks, and they take the shot right in the moment when the leg is extended and about to touch the ground again because they want it looking as flat as possible (no knee action). Jumpers want a more powerful jump with more bascule, hunters want a flatter more 'pleasant'-looking jump with snappier knees. Most breeds want photos where the inside leg is in motion or forward because it makes the shoulder look more sloping, since the shoulder blade rotates back when the horse lifts its leg, and a more sloping shoulder makes for a longer stride and is generally considered more desirable.
Another example, IMAGINE these are nice photos and not video stills hahahaha
This is a nice-enough photo of my horse set up for Arab halter. His back legs are split, his neck is lifted and curved (ish, he's not perfect but he was really rusty :P), his front legs are inched ever so slightly forward and he's rocked back slightly to improve his shoulder angle
vs if it were a photo taken one second earlier, before he rocked back, it'd be uuugggggly ugly.
If the handler STARTS to lift her hands or makes the slightest move forward, she's rocking the horse back, and usually they rock too far back first and then even it out and stretch EVER so slightly forward again, and right when they start to stretch forward again is the moment to snap the photo. Otherwise you waste a bunch of space on your card and end up with 8 blah photos and the one good one, whereas if you know your timing you can cut to the chase and just get the one good one. :P
The show photographer at the last show we did had terrible timing and didn't get any shots while he was nicely set up at all, and I bought nothing where I went to the show totally excited for pictures and prepared to buy a few of the best.
So it can get pretty technical depending on the breed and the section of the horse world you're catering to. A life full of horses puts you ahead of the game for sure.
Like I said, I doubt it makes a difference for art photography, of course, and sometimes people do want nice artsy shots but even that differs by breed / what different breeds consider desirable. Most horse people want shots that first and foremost show the horses off in their best light + make them look closest to their breed standard, and serious horse people tend to be very picky. Backyard/trail riders probably care less about the technical stuff overall, but again that depends, I know some who are very picky and still want to delete any pic ex. in the last phase of the canter where the horse is on its inside foreleg and the weight is on the forehand, it's almost universally considered ugly. I did a quick google search to get one to show you what it looks like and didn't even see one on the first SEVERAL pages because everyone immediately deletes them, lol!!
I could basically go on for days, sorry this is so long XD