article class the bibliography (either input directly as a
thebibliography environment or prepared with the help of BibTeX or Biber) is considered as an unnumbered section, so there's no page break.
report class it is considered as a chapter, which makes sense, because the higher level of subdivision is precisely the chapter.
For a paper the
article class is recommended. However one can obtain the same effect in
report by following the method outlined in the answer Start new chapter on same page
(although I find it disputable to have no break between the last chapter and the bibliography, because this would mean that the bibliography is relative to the last chapter only).
Take your pick.