With the exception of, e.g., part title pages and chapter starting pages, memoir by default uses the headings pagestyle. The style definition can be found in section 7.3 of the manual; use \makeevenhead & friends to change it. The command syntax is \make<even/odd><head/foot>{<style>}{<left>}{<center>}{<right}.
EDIT: I also included a new plainnotice style (derived from plain) that is used for chapter starting pages. Part title pages will still use the plain style.
EDIT 2: For "special" chapters like the bibliography one may define a special pagestyle like headingsnobook (e.g., resembling the original headings style) and switch to it via \pagestyle{headingsnobook}. (The starting pages of "special" chapters will still use plainnotice.)
\documentclass{memoir}
\makeevenhead{headings}%
{\thepage}{}{\slshape\bookname~\thebook\qquad\partname~\thepart\qquad\leftmark}
\makeoddhead{headings}{\slshape\rightmark}{}{\thepage}
\makeevenfoot{headings}{}{}{(Copyright notice)}
\makeoddfoot{headings}{(Copyright notice)}{}{}
\copypagestyle{plainnotice}{plain}
\makeevenfoot{plainnotice}{\thepage}{}{(Copyright notice)}% not used with "openright"
\makeoddfoot{plainnotice}{(Copyright notice)}{}{\thepage}
\aliaspagestyle{chapter}{plainnotice}
\copypagestyle{headingsnobook}{headings}
\makeevenhead{headingsnobook}{\thepage}{}{\slshape\leftmark}
\usepackage{lipsum}
\begin{document}
\book{The first book}
\part{First}
\chapter{First-first}
\section{First-first-first}
\lipsum[1-10]
\part*{Backmatter}
\pagestyle{headingsnobook}
\begin{thebibliography}{9}
\bibitem{test}\lipsum[1-10]
\end{thebibliography}
\end{document}