How to make bread mould resistant?

There are many "natural" or "clean label" ingredients that work as mold inhibitors. Most of them work by adding some acid and thereby creating a more inhospitable environment for mold. Some of the popular mold inhibitors (at least is some U.S. bakeries) are: cultured whey, vinegar, and raisin juice.

I think vinegar and raisin juice are good options for home use.

Vinegar

Works by adding Acetic acid. The white vinegar you buy in the grocery store is typically 5% acetic acid (at least in the U.S.).

To inhibit mold, the recommended amount is 0.5-2.0% of the flour weight of 5% acetic acid vinegar. Add with your other liquids.

Raisin Juice Concentrate

Raisin juice concentrate has been shown to be effective at retarding mold and bacteria growth in bread. It works by adding Propionic acid and Tartaric acid. Further, it seems that a home baker should be able to purchase this in reasonable quantities and at a reasonable price.

The recommended amount is 5-10% of flour weight, by weight. Add with your other liquids.

My personal experience is positive: I used to purchase a whole-wheat bread with raisin juice concentrate and it lasted forever.

This study from the Journal of Food Science, Application of raisin extracts as preservatives in liquid bread and bread systems, found very dramatic increase in shelf life.

The mean mold-free shelf life of the bread containing 7.5% water extract [of raisins] was 18.1 +/- 3.3 d at room temperature while the negative control was mold free for 9.4 +/- 2.4 d. The antifungal efficacy of the extracts in bread was equivalent to 0.24% calcium propionate in 21 d of storage. Doubling the concentration of the extract did not improve the mold-retarding property in bread. The bread containing raisin paste, the percentage of which in dough was equivalent to 15% raisin extract, exhibited a stronger antifungal activity than did the extracts in bread.

Notes

Both of these can inhibit yeast activity which you may need to compensate for by increasing yeast or proofing time.

Sources: some personal experience, this really interesting article from Oklahoma State University, Clean Label Mold Inhibitors for Baking, and the study linked above.

The most common ways to naturally extend the shelf life of bread are to change its enzymatic activity, available water, or pH.

There are a variety of enzymatic shelf life extenders such as Naturelle, Mold Out, Bred Mate II, etc. Most of these are made of a cultured carbohydrate base, such as wheat flour, corn starch, or corn syrup. They are added to dough at around 1-2% of the flour weight and will usually extend the shelf life of bread by a few days.

Preservatives that lower the available water are usually made of a carbohydrate that will bind with the water, commonly listed as "fruit juice and grain dextrins" or another form of dextrins. These work by making less water available for mold growth which requires an available water level of around 0.7. These can have the added benefit of slowing staling.

A final method to make your bread more mold resistant is to lower the pH. This is best done by culturing the dough with a sourdough culture or an acidic preferment and giving it a long proof time for the microorganisms to acidify the dough. This could theoretically be achieved through using ascorbic acid or citric acid, but is next to impossible to do in practice. Citric acid has a strong lemony flavor and has the effect of breaking down gluten, while ascorbic acid has a bitter flavor and makes gluten very tight. The levels at which both acids affect gluten is far below the level that they would have an acidifying effect on the dough. A better solution would be lactic acid which is produced in sourdough cultures (as well as many other cultured foods). The flavor of lactic acid is more complementary to bread and the acid won't have an overwhelming effect on dough workability at practical levels.

Ascorbic acid is the most common way of making bread - and many other things - mould resistant. It is a naturally occurring compound, and one of the forms ("vitamers") of vitamine C.

My problem with ascorbic acid, is that it doesn't do anything for the flavor of the bread. I have seen recipes that call for wasabi, which is said to impart many of the same preservative properties, while adding a faint flavour to the finished loaf.

Factory bread contains ascorbic acid as a preservative. While usually made artificially from glucose, it does occur in nature, in fruits that contain vitamin C for example.

You can add that to your bread.