After helping Bonnie with the Ranch in Red Dead Redemption, get a good night's sleep and head to her house, which you can find by the marker on the map. Upon entering, watch a cutscene after which the Woman will challenge you — who among you is the more experienced rider. Saddle your horse and start the race. Since the track you need to run on will be marked by fire with smoke, and the main character's horse is much faster than the rival's, it will be easy for you to win.
For completing this mission, you will receive +10 points in the Fame category.