A bread pudding, often cooked slowly in a bain marie or water bath, has a nice, light texture, and is generally served warm. We think if you cook it ahead, refrigerate it, and then reheat it, you will lose a lot of the appealing texture. It will still taste good, but will probably be a lot denser, maybe even gloppy.
If you make it ahead, it might be best to take it out of the refrigerator an hour before serving and serve it at room temperature, rather than popping it back in the oven with the risk of overcooking the eggs and making it tough. You would not want to make it more than two or three days ahead in any event.