Preheat the oven to 350°. Lightly butter a 1-quart shallow baking dish and arrange the croissant pieces in the dish. In a small saucepan, stir the sugar and water over moderately high heat until the sugar dissolves; wash down any crystals on the sides with a wet pastry brush. Cook without stirring until a medium amber caramel forms, about 5 minutes. Remove from the heat and stir in the cream, milk and bourbon. Cook over low heat just until any hardened caramel dissolves.
In a bowl, whisk the eggs. Gradually whisk in the hot caramel. Pour over the croissants and let stand for 10 minutes, pressing the croissants to keep them submerged.
Bake the pudding in the center of the oven for 20 minutes, until puffed and golden. Let cool for 10 minutes, then serve.