Horse bonding in Rockstar Games' Red Dead Redemption 2 is of utmost importance, seeing as it can lead to players either forming a unique bond with one of their horses/steeds/mounts or being left out to dry when their companion leaves them in the wilderness after being scared by a bear. In order to attain the former, players must develop a bond with their horse in Red Dead Redemption 2, which in turn grants the player enhanced abilities, such as being able to call their horse by whistling from far-off distances.
In Red Dead Redemption 2, there are four levels for horse bonding; each level coincides with different attributes. Level 1 is devoted to increasing a horse's health and stamina; Level 2 allows players to call their horses from greater distances and while in combat; Level 3 enables horses to traverse more intense terrain, including deeper water, and Level 4 makes players' horses much more difficult to steal. It's worth noting that each horse has their own unique bonding levels, thus meaning that a horse that has been bonded up to level 3 won't have those attributes transferred over to a new horse that players just purchased.
Increasing a horse's bond in Red Dead Redemption 2 isn't particularly difficult (in order to interact with your horse, walk up to it and use the left trigger), but it does take time. It's not something that can be done right away and, while the bonding level appears to naturally increase over time, it's best if players spend a few extra minutes every now and then taking care of their horses. Think about it this way: how would people bond with horses in real-life? They would feed the horses, groom it, etc. That's exactly what players need to do in Red Dead Redemption 2.
To start off, make sure that the horse is groomed, which should be done if the horse is dirty or has recently traveled a lot. And if players are traveling great distances, always make sure that the horse is well-fed and rested. If need be, camp out somewhere for the night. Continuing off that point, make sure to monitor the horse's stamina levels. If the horse is tired, take a moment to stop and feed it. In fact, one way to naturally increase a horse's bond over time without doing much is to make sure that it doesn't tire out. Galloping, especially while carrying something (a person, a pelt, etc.) stowed on the back of the horse will tire it out very fast. So, instead of galloping all the time, ride at a canter.
One of the least but most important things players can do in order to not only increase their bond levels with a horse but make sure that their bond isn't hindered is to make sure that the horse isn't put in any danger. This could be as simple as hitching the horse somewhere and going hunting without it following or even calming it down whenever the horse becomes agitated, which can and does happen quite often. Bottom line: there's no one-step process to increase a horse's bond, but there are only a handful of things that players need to do in order to push it forward.