As general words of advice, I would recommend that you be prepared to discuss Elizabeth Bishop’s poems in terms of two critical approaches, the New Critical and the biographical.
The New Critical approach: The New Critical approach looks at poems as poems. Nothing outside the poem needs to be considered, and what is perhaps most important is to be able to identify themes, irony, and a complex unity within the poem. To prepare for a New Critical approach, practicing talking and writing about the individual poems as poems. Be able to describe the overall form of the poems and, if there is a person in a particular poem, call that person the “speaker,” not the narrator and especially not the poet herself. For example, “A Miracle for Breakfast” is a sestina, and “Argument” is written in free verse. The person who appears in the opening lines of “A Miracle for Breakfast” (“At six o'clock we were waiting for coffee, / waiting for coffee and the charitable crumb”) or in line 5 of “Argument” (“argue argue argue with me”) is the speaker in the poem.
The biographical approach: The biographical approach is quite different from the New Critical in that it looks outside the poem for meaning. The biographical approach is interesting for Bishop’s poems because she was part of an important group of American poets: she was strongly influenced by Marianne Moore and, in turn, her poems “The Fish” or “The Armadillo” reportedly had a strong influence on Robert Lowell’s “The Skunk Hour.” At the same time, though, her poetry often does not have the “confessional” (or intensely, sometimes even embarrassingly personal) quality that is found among many of her fellow poets. The biographical approach can include reading Lowell as a woman poet and/or as a lesbian poet, although she seems to have resisted those sorts of labeling of her work.
If you have specific poems that you think might appear on the exam, I would encourage you to post questions on them. I hope that this answer is helpful.