How could I reheat this the next day? Or is it better to serve cold?

I have always sliced it and fried it in butter. Serve it with syrup or fruit, omg

I actually do reheat bread pudding. Assuming you've served some of it, leaving your baking pan no longer full, I'd transfer it to a different (buttered) baking pan and then baked it, probably covered with foil, at 350 for 10-20 minutes, until quite warm/hot. I don't think it'll dry out, but you could always serve it with cream, whipped cream or ice cream if it did.

I just had to thank you for the question because I missed this recipe and it looks divine!

2nd day I would serve it at room temperature. Which is not "cold." To me, "cold" means served directly from the refrigerator. Almost no food tastes its best at that temp because cold muffles the flavor. Most food projects maximum flavor at room temperature. (yes, I know, it's not supposed to be "safe" to eat food at that temp, but fact is fact. ;) My mom made lots of bread pudding for us when I was growing up. Even freshly baked, she served it just barely warm. It's heavenly like that, imho.