I think the following example might offer some clarity. Consider the following phrases:
The color red
The red color
These are both grammatically correct, but they mean different things. "The color red" refers to the abstract idea of red, while "the red color" refers to a particular instance of something that is colored red.
The color red symbolizes passion.
The red color in blood is caused by the presence of hemoglobin.
Now in your examples, "the word 'bread'" refers to the word itself as an abstract idea, while "the buy one get one free offer" refers to some actual, particular offer at a store.
As an aside, I think you could correctly say "the offer 'buy one get one free'" in the right context, although it might not be the clearest choice of wording. For example,
The offer "buy one get one free" was invented by Roman merchants in the second century CE.
In this situation I would probably write "the offer of 'buy one get one free'". This is because BOGOF is not the name of the offer exactly, it's more like a description of what the offer is.