Preheat the oven to 375 degrees F and position a rack in the center of the oven. Grease a 2-quart baking dish with butter and set aside.
In a large bowl, combine the cubed bread, sugar, eggs, cinnamon, vanilla, salt, melted butter and milk; mix thoroughly, then transfer to the prepared baking dish. Pour in the bourbon, and gently fold in the cherries.
Place in the oven and bake until puffed and golden brown on top, about 45 minutes. Set aside and let cool completely.
Pour the vanilla glaze over the bread pudding and serve.
Place the confectioner's sugar in a medium bowl. Gradually whisk in the melted butter, vanilla and bourbon until completely combined and smooth. Taste for bourbon; add as needed.