Remove page number from just one (float) page?

There are two ways: use afterpage or put \thispagestyle{empty} inside the figure environment as commented by Peter.

\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{afterpage}
\usepackage{lipsum}
\begin{document}
Here is some text with an equation in it: $f(x)=x^2+3x_0\cdot\sin x$
and the textual content continues into the second line. No other math
content is contained within this paragraph.

\afterpage{%
\thispagestyle{empty}
\begin{figure}
\centering
\includegraphics[width=\textwidth]{images/rlexample.png}
\caption{---}
\label{rlexample}
\end{figure}
}

Here is some text with an equation in it: $f(x)=x^2+3x_0\cdot\sin x$
and the textual content continues into the second line. No other math
content is contained within this paragraph.

\lipsum[1-10]

\begin{figure}
\thispagestyle{empty}
\centering
\includegraphics[width=\textwidth]{images/rlexample.png}
\caption{---}
\label{rlexample}
\end{figure}
\lipsum[11-20]
\end{document}

Note: Putting thispagestyle{empty} inside figure environment may need some \clearpage at appropriate places and may not work properly if [p] in \begin{figure}[p] is used as noted by Enrico. I would advice the use of afterpage though.

The code supplied in comment:

\documentclass[a4paper,12pt,oneside]{article}
\usepackage[utf8]{inputenc}

\usepackage{enumerate}
\usepackage[demo]{graphicx}
\usepackage{afterpage}
\usepackage{lipsum}
\usepackage{filecontents}

\begin{filecontents}{\jobname.bib}
@misc{B02,
  author = {Buthor, B.},
  year = {2002},
  title = {Bravo},
}
\end{filecontents}

\title{42}
\author{Jane Doe}
\date{June 2011}

\begin{document}

\maketitle

\section{Introduction}

\subsection{text}

text text \cite{B02} texttext text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text text

\afterpage{%
\thispagestyle{empty}
\begin{figure}[p]
\centering
\vspace*{-3cm}
\includegraphics[scale=0.4]{image.jpg}
\caption{caption}
\label{rlexample}
\end{figure}
\clearpage
}

\lipsum[1-10]


\bibliographystyle{plain}
\bibliography{\jobname}
\end{document}

First add the package \usepackage{floatpag}.

Then you can use \thisfloatpagestyle{empty} within the figure environment. This will provide an empty page where the figure is.