The headings for \printbibliography and \printshorthands are defined via \section* (for article-like classes) or \chapter* (for report and book-like classes).
Whether or not a page break is inserted before a \chapter* or \section* is up to your document class.
We can stop LaTeX from breaking a page though, by temporarily disabling the commands that would do that. (See @egreg's answer to Remove pagebreak after a chapter (Only for one chapter!))
In your case that would probably be
\printshorthands
\begingroup
\renewcommand{\cleardoublepage}{}
\renewcommand{\clearpage}{}
\printbibliography
\endgroup
Now the page break before the normal bibliography is suppressed.
In a full MWE
\documentclass[british]{book}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber,style=authoryear]{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\cite{worman,geer,kant:kpv,brandt,cicero,baez/article}
\printshorthands
\begingroup
\renewcommand{\cleardoublepage}{}
\renewcommand{\clearpage}{}
\printbibliography
\endgroup
\end{document}
One could of course, alternatively fake the entire \section* or \chpater* command save for the page break and use that to define a new bibliography heading that we use for \printbibliography.
The command \npbchapter is \chapter with the page break surgically removed, we also define a new bibheading for biblatex
\makeatletter
\newcommand\npbchapter{\global\@topnum\z@
\@afterindentfalse
\secdef\@chapter\@schapter}
\makeatother
\defbibheading{npbbib}[\bibname]{%
\npbchapter*{#1}%
\markboth{\MakeUppercase{#1}}{\MakeUppercase{#1}}}
use this as in
\printshorthands
\printbibliography[heading=npbbib]
MWE
\documentclass[british]{book}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber,style=authoryear]{biblatex}
\makeatletter
\newcommand\npbchapter{\global\@topnum\z@
\@afterindentfalse
\secdef\@chapter\@schapter}
\makeatother
\defbibheading{npbbib}[\bibname]{%
\npbchapter*{#1}%
\markboth{\MakeUppercase{#1}}{\MakeUppercase{#1}}}
\addbibresource{biblatex-examples.bib}
\begin{document}
\cite{worman,geer,kant:kpv,brandt,cicero,baez/article}
\printshorthands
\printbibliography[heading=npbbib]
\end{document}
biblatexcitations. – moewe May 31 '15 at 09:42geometry. I used a different approach as my thesis template conflicted with geometry, but I can't find an easy link. You'd get a page break but no blank page (which are you trying to avoid?) This does of course assume you're double-sided to start with, but that seems quite likely (and also explains why a full MWE is a good idea) – Chris H Jun 02 '15 at 14:34