Given the code below, the missing piece of the puzzle is to determine the width of the bounding box from within (which should be less cryptic than from outside).
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{backgrounds, calc}
\begin{document}
\newlength{\myl}
\begin{tikzpicture}
\draw (-2,-1) rectangle (2,1);
\begin{pgfonlayer}{background}
\path[fill=red](current bounding box.south west)rectangle(current bounding box.north east);
\end{pgfonlayer}
%\settowidth{\myl}{current bounbind box.width} % HOW TO?
\coordinate (sw) at (current bounding box.south west);
%\node[black,above right] at (sw) {\the\myl}; % (0pt)
\node[above right,
text width=5em
% text width=\myl
] (bottom) at (current bounding box.south west) {\color{black}
%\makebox[\myl]{%
A\hspace*{\fill}Z
%}
};
% UPDATE:
\path (bottom.north west) coordinate (SW);
\node[black] (SW) {SW};
\end{tikzpicture}
\end{document}
UPDATE # 1:
Subsidiary question, I would have expected SW north-west of the bounding box of (A)--(Z): why is it so far off?
UPDATE # 2: Here's a clarification
\node[above right,
text width=5em
% text width=\myl
] (bottom) at (current bounding box.south west) {\color{black}
\frame{\makebox[5em]{A\hspace*{\fill}Z}}
};





