The suggestion from John really helped. Separating the \footnotemark from footnotetext and combining it the way seen in this answer worked for me:
\documentclass{report}
\usepackage{pdfpages}
\usepackage{bytefield}
\begin{document}
\begin{bytefield}{32}
\bitheader{0,15,31} \\
\begin{rightwordgroup}{\textbf{header\footnote{Some explanation}}}
\bitbox{16}{Magic bytes} &
\bitbox{16}{Size\footnote{size of header}}
\end{rightwordgroup} \\
\end{bytefield}
\newpage
\setcounter{footnote}{0} % reset for demonstration purposes
\begin{bytefield}{32}
\bitheader{0,15,31} \\
\begin{rightwordgroup}{\textbf{header\footnotemark{}}}
\bitbox{16}{Magic bytes} &
\bitbox{16}{Size\footnotemark{}}
\end{rightwordgroup} \\
\end{bytefield}
\addtocounter{footnote}{-2} % we used \footnotemark how many times above?
\stepcounter{footnote}\footnotetext{Some explanation}
\stepcounter{footnote}\footnotetext{size of header}
\end{document}
The first bytefield environment (page 1) shows the issue I had, the second (page 2) shows the workaround.
\footnotemarkand\footnotetextwill work? – John Wickerson Jun 04 '14 at 15:35