It is interesting how the prerequisite to the political life is the bare life yet this bare life is what is technically being excluded from the political life. This delicate balance is what Agamben constitutes as a relationship between the bare life and the political life. It is another example of the common postmodern trend to be as complex as possible and exist in a state that sounds contradictory.
The political life also ties into the bare life for the simple reason that politics has to do with individuals in their most natural, animalistic sense. It is politics that makes the bare man into one who is able to differentiate between good/bad, justice/evil, etc.
So yes, of course the political life and the bare life is tied together in this way that they depend on each other for their own definition. However, does that really mean that they possess a separate relationship beyond this?