For your consideration ...
The question however was if both are primarily influenced by transportation costs for their corresponding increase in price, why aren’t the percentage increases the same?
I am not sure that it is the case at all, that both are primarily influenced by transportation costs. Bakeries are usually centrally located within, or very near, major metro areas, making delivery costs to stores less energy use intensive. Cucumbers can be shipped by the trailer load from farms to metro/sub-metro produce distribution centers where they are bought by local stores and merchants, again with lower overall delivery energy costs.
I would say that the price differential is from the added labor costs, in addition to, for bread making, the physical infrastructure that is needed; large real estate holdings, huge buildings, lots of ovens using either electricity or natural gas, conditioners, mixing, fermentation, makeup, proofing, baking, cooling, slicing and packaging. Uses more labor, has higher operating costs, more regulatory hurdles, higher taxation costs due to real estate valuations, etc.. Add, that bread's ingredients costs are raising, flour, dairy, etc.. With each ingredient itself needing processing, to some degree, into a final product before being used as an ingredient to make bread.
With cucumbers, mechanically picked, after harvest, place a certain number in a produce box, fill a trailer, and ship off to the commercial produce market, where orders are placed by local area stores which is then delivered by produce refrigerated trucks.
Both are delivered from a given central location, so delivery costs, fuel required, should be somewhat equal.