MWE
\documentclass[a5paper,11pt]{book}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{verse}
\usepackage{showframe}
\begin{document}
\newcommand{\attrib}[1]{%
\nopagebreak{\raggedleft\footnotesize\textit{#1}\par}}
\poemtitle{Fleas}
%\settowidth{\versewidth}{You can’t tell a he from a she.}
\begin{verse}%[\versewidth]
What a funny thing is a flea. \\
You can’t tell a he from a she. \\
But he can. And she can. \\
Whoopee! \\
\end{verse}
\attrib{2015}
\newpage
\poemtitle{Fleas}
%\settowidth{\versewidth}{You can’t tell a he from a she.}
\begin{altverse}%[\versewidth]
What a funny thing is a flea. \\
You can’t tell a he from a she. \\
But he can. And she can. \\
Whoopee! \\
\end{altverse}
\begin{altverse}%[\versewidth]
What a funny thing is a flea. \\
You can’t tell a he from a she. \\
But he can. And she can. \\
Whoopee! \\
\end{altverse}
\attrib{2015}
\end{document}
But, That I want,

All the poems at the bottom of the pages. And poems are flushleft. The date, flushright.
How is it changing macro in my MWE?
I have only one problem. Here the picture. White space in poems.

\mbox{}\par\vfill \poemtitle.... However, your question isn't quite clear in that regard. – Werner Jun 22 '15 at 16:53\null\vfillbefore the poem. – Thérèse Jun 22 '15 at 17:00\vspace*{\fill}is the preferred LaTeX way. – egreg Jun 22 '15 at 17:10\raggedrightrather than\raggedleftfor right-aligned dates? – cfr Jun 22 '15 at 17:14\setlength{\leftmargini}{0em}to remove the unwanted space at the beginning of the lines. – Thérèse Jun 22 '15 at 17:28texdoc versepage 7 to do what @Thérèse suggests in a way which does not affect all list environments (which includes a lot of things you probably don't realise are lists). – cfr Jun 22 '15 at 17:29