To get a grip on keeping bread after baking, you have to understand that bread going stale is not just a matter of it drying. The bread continues to undergo internal changes after baking. It is thought that starches are altered in baking so that they absorb water, and during storage, the starches revert somewhat to the former state and release water. The water is taken up by the gluten, changing the bread's texture. And, understandably, the crust, being dry, draws water from the interior, changing both crust and crumb.
Storing bread in the refrigerator speeds those changes. (Freezing does not, but that's a different longer-term storage.) So, water is moving around, and changes are taking place. You can see why a tightly sealed bag encourages mold in the crust as it takes on water. A cloth bags and ventilated bread boxes are about as good as you can do, and both are really no better than leaving it out, except for bugs and dirt and such (and the temptation of seeing fresh bread every time you walk by - but fresh bread being out in a kitchen sure looks homey).
Plastic bags can do nothing to retard the natural changes going on and can merely encourage mold. The phrase, "day-old bread" means something. Most breads do not keep well beyond the first day. The may be palatable on the second or even third day, but they are not unchanged. So that's subject to the individual's tolerance. Second-day bread is, however, almost always fit for toasting, if done at a high enough temperature to reconvert the starches, which reverses many of the changes we interpret as having gone stale.
Different breads do better after baking. Baguettes and other lean dough breads don't last long. Wet dough breads last a bit longer.
And, of course, we understand we're not talking here about the chemically engineered abominations sold in supermarkets as plastic-bagged bread in a partially cooked state to give it "shelf-life."
"Kitchen duty is awarded only to those of manifest excellence..." - The Master, Dogen