If I understand your question correctly, you want to have a kind of title for your questions and that title should be bold-faced, In this case, you can define a new theorem style and use the note field (the optional argument) to get the desired result:
\documentclass{article}
\usepackage{amsthm}
\usepackage[framemethod=tikz]{mdframed}
\newtheoremstyle{mystyle}
{\topsep}%
{\topsep}%
{\itshape}%
{}%
{\bfseries}%
{.}%
{.5em}%
{\thmname{#1}~\thmnumber{#2}\thmnote{. \bfseries#3}}%
\theoremstyle{mystyle}
\newtheorem{question}{Question}
\mdfdefinestyle{que}{
linecolor=cyan,
backgroundcolor=cyan!20,
}
\surroundwithmdframed[style=que]{question}
\begin{document}
\begin{question}[Lorem]
Text
\end{question}
\begin{question}
Text
\end{question}
\end{document}

If, on the other side you want all the contents bold-faced, you have two options:
If you are not using amsthm, simply add font=\bfseries to the mdframed specifications:
\documentclass{article}
\usepackage[framemethod=tikz]{mdframed}
\newtheorem{question}{Question}
\mdfdefinestyle{que}{
linecolor=cyan,
font=\bfseries,
backgroundcolor=cyan!20,
}
\surroundwithmdframed[style=que]{question}
\begin{document}
\begin{question}
Text
\end{question}
\end{document}
If you are using amsthm, you'll need to add the specification to the theorem style:
\documentclass{article}
\usepackage{amsthm}
\usepackage[framemethod=tikz]{mdframed}
\newtheoremstyle{mystyle}
{\topsep}%
{\topsep}%
{\bfseries\itshape}%
{}%
{\bfseries}%
{.}%
{.5em}%
{}%
\theoremstyle{mystyle}
\newtheorem{question}{Question}
\mdfdefinestyle{que}{
linecolor=cyan,
backgroundcolor=cyan!20,
}
\surroundwithmdframed[style=que]{question}
\begin{document}
\begin{question}
Text
\end{question}
\end{document}

Notice that italics plus bold-face might not be the best choice.
Loremto be bold? – Werner Feb 23 '14 at 19:25font=\bfseriesto the style definition should do – cgnieder Feb 23 '14 at 19:27\newmdtheoremenvcommand as described in Section 8 of the »mdframed« manual. – Thorsten Donig Feb 23 '14 at 19:38