You should be using \input
not \include
. The latter adds a \clearpage
. Here is the first example from the AMS documentation in your set-up:

Main file:
\documentclass{article}
\usepackage{amsrefs}
\begin{document}
Alan Sokal~\cite{Sokal96} recommends Bourbaki’s text~\cite{Bourbaki70}
for a gentle introduction to set theory.
\begin{bibdiv}
\begin{biblist}
\input{bibcode}
\end{biblist}
\end{bibdiv}
\end{document}
with bibcode.tex
containing:
\bib{Bourbaki70}{book}{
title={Th\'eorie des ensembles},
author={Bourbaki, Nicolas},
date={1970},
publisher={Hermann},
address={Paris}
}
\bib{Sokal96}{article}{
title={Trangressing the boundaries},
subtitle={Toward a transformative hermeneutics of quantum gravity},
author={Sokal, Alan},
journal={Social Text},
volume={46/47},
date={1996},
pages={217--252}
}
amsrefs
– daleif Sep 13 '13 at 13:01