To find out a book that contains any references to Maya Angelou would you use an index or bibliography?

You would use an index, if I understand your question correctly. A bibliography is a list of books: you could have a list of books that contain information about Maya Angelou but to make that list you might have to consult an index to see if the book had information on her so you could include it in the bibliography. An index is a list of topics found in one book. Confused? ;-) Hope not!