The traditional essay is a formal writing genre. It does not permit bullets or even such casual usages as contractions. However, (there's always a however in discussions of writing), the place where you intend to publish your essay may not be so formal.
Check the writer's guidelines to be sure.
If you are writing an academic essay for a college course, visit any reputable university online writing lab website for information about standards. (The OWL at Purdue University is one of the outstanding ones.)
