If you cannot see a Stallion in your list, we need to check a couple of options for that in your database.
Navigate to Main > Horses and search for the horse in question. Double-click to open the horse details screen.
For a stallion to be available for bookings, the horse needs to be set as a Current Horse, set as Type: Stallion and preferably also be ticked as Standing at Stud.
Save/update your changes, and try again through the Bookings screen.