Exciting news for bread lovers! The researchers at Monash University recently analyzed sourdough products, and discovered that many types of sourdough wheat products are low in FODMAPs. From The Well Balanced FODMAPer:

Tips to help you select the most likely low FODMAP sourdough bread option:

First, check ingredients! Some sourdough bread products contain FODMAPs such as high fructose corn syrup or honey. Though most of the sugar in these sweeteners would be consumed by the yeast and bacteria in the sourdough culture, check the nutrition fact label to evaluate for the present of any residual sugar. Try to select bread with zero sugar on nutrition fact label.
Call the company and ask if their sourdough bread is a slow rise product. Do they allow it to naturally leaven for 1-2 days? (UPDATE: I contacted the following bakeries in Seattle: Grand Central, Macrina, Tall Grass, and Essential. All of their sourdough breads should be low FODMAP.)
Look for yeast in the list of ingredients–which is often used to speed up the leavening–and the best option to allow for the greatest reduction in FODMAPs is a slow leavening process. In other words, it is the slow rise or slow fermentation that allows for the reduction of FODMAPs. Yeast is often added to speed up the process, so less time to reduce the FODMAPs.
Of course, we don’t know for sure what the FODMAP content of a bread is without analyzing it! Hopefully more companies will have their products evaluated by Monash University low FODMAP Certification program.