You can obtain him when you give the 5 pieces of Bucephalus's legendary tack to one of your horses, or when you purchase a Bucephalus pack.
On most days, you will not be able to stroke him, but on certain days he will allow you to. When stroked, he gives a +3 Dressage bonus to all the horses you currently own. This bonus is available until the next daily update. This bonus does not stack.
When Bucephalus is obtained via the Bucephalus pack, you can stroke him more often.
Game: provides a Dressage +3 bonus to all your horses (until the next daily update) when stroked
VIP: Bulk horse registration in equestrian centers.
This horse cannot be sold.