Make your way over to Valentine to meet up with Sadie in the saloon as you intervene in the ruckus. Sadie asks for your assistance in a bounty and the two of you ride off to Strawberry.
Once you gain control in town, you’ll have 30 seconds to find the bounty so dash as quickly as possible to the northern most house, the Welcome Center, and head upstairs to room 3. After knocking on the door, kick it down and the bounty will escape out the window, jump over the balcony yourself and mount up.
You now have 1 minute 15 seconds to catch up and Lasso him and he’s a deceptively fast rider. The easiest way to go about this is to take a gun out, enter Dead Eye and shoot the horse in it’s back leg to slow it down (or outright kill it if you don’t mind the Honor loss). You can then simply gallop over to it, Lasso the bounty and hogtie it with plenty of time to spare.