Butter 6 slices cinnamon swirl bread, then place them butter-side down into a casserole dish. Butter 6 more bread slices and place them butter-side down on the other slices.
Mix together milk, eggs, sugar, vanilla, and salt in a bowl until smooth and pour over bread in the casserole dish. Cover and place in the refrigerator for 8 hours to overnight.
Preheat the oven to 350 degrees F (175 degrees C).
Place the casserole dish inside a larger pan; pour water into the outer pan, making sure not to get water in casserole.
Bake in the preheated oven until a knife inserted into the center comes out mostly clean, about 50 minutes.