Assuming that you are not using in-text citations, you should try to introduce the author's background as naturally as possible. In other words, try not to disrupt the "flow" of your sentence. For instance, with the first example you gave,
Charles Bazerman's, the author of "A Relationship Between Reading and
Writing: A Conversational Model, argument was that….
you cut off the explanation of his argument in order to provide background information, which is not good; you want to introduce his background before providing his argument and, preferably, without separating the author's name or source title from the quote.
So, try something more like this:
In A Relationship Between Reading and Writing: The Conversational Model ,
Charles Bazerman argues that "blah blah blah…."
See how the author's name is closer to the actual quote, and there's no information in-between?
If you're not quoting from his book (i.e. you want to mention what the author's best known works are, without quoting those works), you should consider splitting the background information into two sentences, like this:
Charles Bazerman, author of A Relationship Between Reading and
Writing: The Conversational Model, prefers another approach. In "Insert
Generic Article Title Here," Bazerman argues that….
However you insert the background information, try not to insert background information between the title/name of your source and the quote you wish to provide. If that's not possible, try your best not to disrupt the "flow" of the sentence, at the very least.
I hope this helps!