The dragon itself will only use 1 stable slot. The second you're maybe thinking of is to allow you to stable every pet so you can swap between a 5 slot dragon and something else.
Example, if I have a full 14 stable slots used, I could have a 15th pet bonded and logging out with me. But to swap pets in the stables, I'd need to claim a second pet, stable the one I didn't want etc.
If you bond a greater dragon however, you need that extra stable slot at the swap stage, because you can't pull a 1 slot pet from the stables alongside your dragon.
So a tamer who keeps a greater dragon will always be restricted to an absolute max of 14 stable spaces, because they need to be able to stable every pet to swap the greater dragon around.
I hope that makes sense lol.
Wenchy