Bread that never molds

Cliff and I eat very little bread.  It just doesn't work into our meals very well, what with my striving to work seven to thirteen daily servings of fruits and vegetables into our diet.  That isn't as hard as it sounds, since a serving is usually such a minuscule amount that it's easy to double or triple a serving.  For instance, one can of green beans is considered three and a half servings:  Cliff and I divide the contents of the can between us, so we're each getting 1 and 3/4 servings with our meal; the calories are still under forty.  If we're having fresh green beans from the garden, we're liable to quadruple the serving.  Green beans, without any form of fat put on them, have very few calories.  
If you're having a sandwich for your meal, you're not getting many veggies; I don't care how much you try to pile on the sliced tomatoes and iceberg lettuce.
Yesterday we had smothered okra, made with okra and tomatoes from the garden.  Low-fat and nutritious stuff indeed, and we each had about three servings for dinner (if I had measured), and then Cliff had a serving in his lunch box for his evening meal at work.    
So, with all those fruits and veggies, there's hardly room in the meal plan for bread.  When I buy a loaf of bread, I keep it in the freezer and get a slice or two out as needed.  
Three weeks ago, I got out the half-loaf that was in our freezer and forgot to put it back.  After it had set out for a few days, it wasn't so fresh any more, and I decided to do an experiment:  I wanted to see if it would mold, laying on the counter with the bag closed around it.  Because I've noticed over the past few years that bread doesn't mold the way it used to.  I used to buy Sara Lee Iron Kids bread simply because it stayed fresh for a long time,  but when it got to over $3 a loaf, I scaled down to this:  

Even after it was removed from the freezer, the bread was pretty much usable for a week or more.  Now it's getting rather dried out, but there's no mold on it.  I posed a question on Facebook:  "Does it bother anyone else that store-bought bread no longer molds, even if it sits around for two weeks or more?"  
I got more that twenty replies, and most of them were from people, my daughter included, who told me that their bread still gets moldy.  I know my daughter buys store-brand bread: Aldi's, when she shops there.  She has told me Aldi's bread doesn't do very well in the freezer, so maybe it wouldn't work for us.
I'm thinking I need to buy cheaper bread without so many preservatives in it.  Or maybe I should make my own; but home-made bread is very calorie-dense and wouldn't be so good for Cliff's weight-loss program.  
Just look at the ingredients in my plastic bread:  

What is all that stuff?  When I make bread, the ingredients are simple:  milk, flour, salt, yeast, and shortening.  
Of course, since we eat so little bread, I'm thinking I could make my own bread, slice it thin, put it in the freezer, and keep it frozen, getting out a slice or two as needed.  
At least I would know what I'm eating.  


My daughter left a link in my comment section about this very topic.  Click HERE.  
And Inga left a comment saying if we used whole wheat bread, it would mold.  Well, although I prefer it, Cliff WILL NOT eat whole wheat bread.  Unless he's at somebody's house and minding his manners.  He also hates whole wheat spaghetti.  He does like my home-made, low-fat whole wheat muffins, though.  
Inga, I'm pretty sure we get our quota (six ounces) of "bread" each day.  We always have cereal, either hot or cold, for breakfast, or healthy muffins I make... or healthy coffeecake.  We have rice at least four or five times a week, often brown rice, because it's included in so many of the dishes I make regularly.  And then there are recipes that contain bread toppings (my "tex-mex beans with corn bread dumplings, for example).  Yes, we get our six ounces of bread daily, one way or another.