It is true that Bakhtin is known mostly as a Formalist and Marxist literary theorist. One of Bakhtin's most famous works is Discourse in the Novel. In this work, he discusses heteroglossia, the most significant stylistic feature of the novel. Heteroglossia is the multiplicity and internal stratification of language. It is living language: the interplay of social and class dialects, professional jargon, differences in generational speech, and so on. In this respect, the language of the novel is dynamic and dialogic (meaning that it is intertextual). Compare this to a poem, in which the poet presents a unified, monologic description.
How might Bakhtin define reader-response theory in relation to his own work? Consider his analysis of the novel and its many "voices." There are competing and collaborating voices of differing class and social status, historical location, political affiliation, and so on. Each voice connotes certain ways of living, different ideologies, and different perspectives in the novel. It seems logical to assume that Bakhtin would likewise acknowledge the multiple backgrounds/voices of actual readers. Just as the voices in the novel are an example of heteroglossia, so too is the community of readers. The community of readers will interpret said novel in any number of ways, and these interpretations will compete with one another as the community debates what the novel means. Someone reading The Iliad in ancient Greece will have a much different reaction than someone reading it in twenty-first-century Argentina. The type of readers changes over time and place as well.
We might call this the heteroglossia of readers, as it is comparable to the heteroglossia of voices and languages in the novel.