How to shorten \hline in a matrix

The bmatrix environment and also the other matrix related ones use internally array, but do a backup after the left delimiter and before the right one. Therefore the rule made by \hline presents the problem you're facing.

There are technical reasons for using a backup rather than removing the intercolumn spacing at either end with @{}. There are two different solutions; one is to use booktabs and the other one is making a new environment for matrices with rule separators.

The first is more elegant, in my opinion. Both require you to specify the columns in some way.

\documentclass{article}
\usepackage{amsmath}

\usepackage{booktabs} % required for the first solution

% this is for the second solution; the argument is the number of columns
\newenvironment{lbmatrix}[1]
  {\left[\array{@{}*{#1}{c}@{}}}
  {\endarray\right]}

\begin{document}
\begin{equation*}
\begin{bmatrix}
  a & b\\
  \cmidrule(lr){1-2}
  c & d
\end{bmatrix}
\end{equation*}
\begin{equation*}
\begin{lbmatrix}{2}
  a & b\\
  \hline
  c & d
\end{lbmatrix}
\end{equation*}
\end{document}

Try switching to array instead, apparently the bmatrix environment doesn't work well with horizontal lines (judging from what I've seen in other forums).

If you switch between \begin{array}{@{}cc@{}}, as suggested by daleif, \begin{array}{cc}, it will change the appearance.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
    \[ \left[ \begin{array}{@{}cc@{}}
    a & b \\ \hline
    c & d
    \end{array} \right]
    %
    \left[ \begin{array}{cc}
    a & b \\ \hline
    c & d
    \end{array} \right]
    \]
\end{document}