Theoretically the presentation of the citation label in the bibliography is up to the document class you use and can additionally be modified by bibliography-related packages. So it is not possible to say with absolute certainty what you should do.
The following works for most standard setups. In the standard classes the citation label in the bibliography is typeset using the \@biblabel command. It is defiend as \def\@biblabel#1{[#1]} and it is straightforward to add \textbf to make it read
\documentclass{article}
\makeatletter
\renewcommand*{@biblabel}[1]{\textbf{[#1]}}
\makeatother
\begin{filecontents}{\jobname.bib}
@book{appleby,
author = {Humphrey Appleby},
title = {On the Importance of the Civil Service},
year = {1980},
publisher = {Pub & Co.},
}
\end{filecontents}
\begin{document}
\cite{appleby}
\bibliographystyle{plain}
\bibliography{\jobname}
\end{document}
Remember that you need \makeatletter...\makeatother because the macro name contains an @ to mark it as internal. See also What do \makeatletter and \makeatother do?.
