Keep the sliced sandwich bread and bagels in the freezer. PB & J (and any other sandwich filling) spreads nicely on frozen bread, and packs neatly into a sandwich bag. When noontime rolls around, the bread will have thawed, and the sandwich will be perfectly fresh, soft and munchable.
Bonus: Frozen bread keeps an insulated lunch pack cool.
Warning: I’ve tried freezing pre-made PB & J sandwiches, too. Total failure.