To have no pagebreak before Bibliography

Internally, thebibliography environment uses \chapter*; if you want the bibliography to behave like a section, you can patch the \thebibliography command to use \section* instead of chapter*. To do this, add the following lines to the preamble:

\usepackage{etoolbox}
\patchcmd{\thebibliography}{\chapter*}{\section*}{}{}

A complete example:

\documentclass{report}
\usepackage{etoolbox}
\usepackage{lipsum}% just to generate text for the example

\patchcmd{\thebibliography}{\chapter*}{\section*}{}{}

\begin{document}

\lipsum[1]

\begin{thebibliography}{9}
\bibitem{a} Test A.
\end{thebibliography}

\end{document}

If the biblatex package is used to produce the bibliography, one can use \defbibheading to define a heading using \section*:

\documentclass{report}
\usepackage{lipsum}
\usepackage{biblatex}

\addbibresource{biblatex-examples.bib}
\defbibheading{secbib}[\bibname]{%
  \section*{#1}%
  \markboth{#1}{#1}}

\begin{document}

\lipsum[1]
\nocite{*}

\printbibliography[heading=secbib]

\end{document}

If you are using the natbib package, you may try the option sectionbib:

\usepackage[sectionbib]{natbib}

If the biblatex package is used to produce the bibliography, you can also use one of the predefined headings, i.e. subbibliography

For instance:

\printbibliography[heading=subbibliography]

You can refer to section 3.6.8 Bibliography Headings and Environments in the biblatex manual.