Overnight is dramatically better than same-day. After chilling, the custard sets into something impossibly creamy. Make it the day before, refrigerate, and pull it out an hour before serving.
The water bath keeps the heat gentle and even, preventing the edges from overcooking before the center is set. This method keeps the pudding uniform, preventing the edges from becoming rubbery or from the center becoming mushy.
Depending on personal tastes, the bread pudding can be mashed less, with more bread left “chunked” for a traditional bread pudding, or can be made into a near flawlessly smooth pudding with bread-like texture by mashing more. It is purely a matter of preference.