I use this LaTeX code to add a bibliography section:
\bibliographystyle{plain}
\bibliography{bp}
The first page looks fine. It contains the Bibliography title, no header and a list of citations. However on the next page is a header with the title of the previous section. Is there a way to remove this header?
The first page is typeset with pagestyle plain. The following pages have the pagestyle of the rest of the document, which (apparently) you modified using fancyhdr.
In the documentation of fancyhdr, see the \markright and \markleft commands, which can modify the headers in your document. Probably a \markright{} can solve your problem.