You just have to not hold the sprint button/key, and the bird will decelerate to default speed after several seconds (you'll notice it when your stamina no longer depletes). The controls are very basic, and just like FF7, the bird will move on its own and sprint at your command (which in turn means it will slow down to default speed if you're not sprinting). It's NOT an immediate process though, but that might be intended.

The response time and everything are all based upon your stats, but I'm not sure if the Cunning stat, Endurance, or Stamina affect the time it takes for the stamina bar to stop depleting. The content is still too new to have anything really accurate about it... although honestly, you really don't have to worry too much about decelerating in races. 90% of the race, if not the entire time depending on abilities and items, you'll likely be sprinting.