For an overview of the scholarship and a quick sense of the state of the question on her, look the biblical woman you've been assigned up in one or more Bible dictionaries or encyclopedias. For lists of Bible dictionaries and encyclopedias both online and off, with Library of Congress Call Numbers, see the first two boxes here.
Here, for example, are the opening paragraphs of the 16-column entry on Bathsheba in the online Encyclopedia of the Bible and its reception, which sketches her appearance in Jewish and Islamic as well as biblical and Christian interpretation, and in literature, the visual arts, music, and film as well:
