Sheriff Kim decided to agree with tagging along, as long as you could find a good hiding spot for you, herself, and the horses to hide behind while trapping the first centaur you find. Once you had everything, you got out of the sheriff's office, while she placed up a sign on the door, saying that she'll be right back.
To recap everything you had, you had a giant net to trap the centaur, bait to get the centaurs attention, and last, but not least the sheriff of Open Gulch for your protection while you trap it. You found a spot near the railroad yard outside of Open Gulch, where some bandits that the sheriff has captured in the past use it to murder women after tying them to the tracks when a train comes. The abandoned station you see was the perfect hiding spot, while you set your trap, and then hide.