This kind of behaviour is usually fixed by compiling your document more than once.
Every time you compile your document latex reads and writes information to a few different files: \jobname.aux, \jobname.toc, etc. When you use biblatex you run bibtex, or biber, etc to update the bibliography auxiliary files. Once these files are updated, you re-compile the original document which will be able to read the updated reference & citation information.
Assuming that you're using a book or report document class, add the etoolbox package to your document preamble
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
and then use
\appendix
\chapter{List of Publications}
\patchcmd{\thebibliography}{\chapter*{\bibname}}{}{}{}
\begin{thebibliography}{1}
If you're not using thebibliography anywhere else in the document, you could move the \patchcmd{<macro>}{<search>}{<replace>}{<success>}{<failure>} construct to the document preamble. This way you keep document elements and formatting clean.
What is behind this correction? You'll notice that both book and report define the bibliography as a \chapter*, which opens up a new page - exactly what you don't want:
\newenvironment{thebibliography}[1]
{\chapter*{\bibname}%
\@mkboth{\MakeUppercase\bibname}{\MakeUppercase\bibname}%
%...
\patchcmd removes this from the environment. It also typesets the headers with \bibname. Not sure whether this is something you're after. Regardless, it can either be removed (with little hassle, similar to the above correction), or left in.
Of course, if this is the very last entry to your document, and you won't be using a \chapter* anymore, a simple redefinition should also work:
\def\@schapter#1{}
\@schapter is the starred version of \chapter, as defined in latex.ltx. If you have some other \chapter* commands following thebibliography (which is perfectly fine), you could also perform this modification locally by grouping it.
Best Answer
The dominant convention, supported by Chicago, Hart's, and Butcher's, is to put the bibliography after the appendices when setting a book.
However, the conventions governing the order of end matter are much less fixed than those governing front matter, which is partly fixed in legislation. And not only books have appendices and reference lists: some conference series and journals have the appendices following the reference list.