Short-term bread storage
Personally I have had varied results when freezing bread. I have had some that came out wonderfully after a couple of months. I have also had some that after a couple of days came out very dry. Note that when freezing bread, I only freeze fresh, and in a very short amount of time after getting it home. I find that results vary depending on the type and brand of bread.

All that said about freezing, I don't think how you keep the bread for the one day period will affect anything as much as the conditions you describe after leaving home. Bread in a bag in a hot car can be bad but bread in a bag sitting in the sun can be really bad. (Even on a short trip to the market I will not place bread in my car where sunlight can hit it.)

What I would recommend is to use a cooler. When preparing to leave for your trip, line the bottom and sides with frozen ice packs and cover the ice packs with a heavy towel to keep them from direct contact with the bread. Cover the items in the cooler with a towel (a little more insulation). The idea is to keep the bread at a moderate to cool temperature.

I do this whenever I carry foods that I want to keep cool but not in contact with ice packs. It works well for bread, perishables (great for salad greens), etc. 

I also learned that a couple of layers of bubble wrap can be used in place of the towels. I can't take credit for the bubble wrap idea though. When ordering perishable items I noticed that this is how they were shipped.