What role do bondages play in "By the Waters of Babylon"?
It isn't entirely clear what your question refers to, but I am guessing that you are talking about the kind of bondages that John and his people are under. You need to remember the setting of this masterful short story and in particular how the people have forgotten their past and history. This, of course, adds greatly to the impact of the story, as we see a society that we as readers initially think is a kind of stone age civilisation - the text talks of taboos, and presents us with a primal, animistic world with a very basic form of religion:
The north and west and the south are good hunting ground, but it is forbidden to go east. It is forbidden to go to any of the Dead Places except to search for metal, and then he who touches the metal must be the priest or the son of a priest. Afterward, both the man and the metal must be purified. These are the rules and the laws; they are well made.
The repetition of "It is forbidden" in this opening section of the novel reinforces the fact that John and his people are in bondage to ignorance - they do not know the reasons behind these rules and regulations, but just blindly accept them. Of course, the first person narration means that we, as readers, are in bondage to ignorance as the story begins - we do not know the truth of what has happened to this society, but as we read, we share John's journey and his increasing understanding of what has happened, and this is what serves to shock us as readers into taking note of the danger if we, like the "Gods" eat knowledge too fast.