Lualatex and bm package

UPDATE

The patch below has been incorporated into the distributed bm.sty 2016/07/07 v1.2b

---

Here is an update for bm in luatex using classic math font setup. It does not do the right thing for opentype math fonts with unicode-math (where it is not always clear what the right thing should be as most such setups do not include a bold font)

\documentclass{article}
\usepackage{bm}

\makeatletter
\def\bm@test@token#1{%
  \let\bm@next\@empty
  \ifx#1\@@end
  \else\ifx#1\mathchoice
    \let\bm@next\bm@mathchoice
  \else\ifx#1\mathchar
    \afterassignment\bm@mathchar\count@
  \else\ifx#1\mathaccent
    \afterassignment\bm@mathaccent\count@
  \else\ifx#1\delimiter
    \afterassignment\bm@delimiter\count@
  \else\ifx#1\radical
    \afterassignment\bm@radical\count@
  \else\ifx#1\mkern
    \bm@register#1{\muskip\z@}%
  \else\ifx#1\kern
    \bm@register#1\skip@
  \else\ifx#1\penalty
    \bm@register#1\count@
  \else\ifx#1\unvcopy
    \let\bm@next\bm@add
  \else\ifcat\noexpand#1\relax
    \xdef\meaning@{\meaning#1}%
    \expandafter\bm@mchar@test\meaning@""""\@nil#1%
  \else\ifcat.\ifcat a#1.\else#1\fi
    \count@\mathcode`#1\relax
    \ifnum\count@=\mathcode`\'%
      \begingroup\uccode`\~`#1\uppercase{\endgroup
        \def\bm@next{\bm@expand~}}%
    \else
      \ifx\bm@previous\left
        \count@\delcode`#1\relax
        \bm@delimiter
      \else
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        \ifnum\count@>"8000
\Umathcharnumdef\@tempa\count@
\xdef\meaning@{\meaning\@tempa}%
\expandafter\bm@mchar@test\meaning@""""\@nil\@tempa
\else
        \bm@mathchar
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \fi
    \fi
  \else
    \bm@add{#1}%
  \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
  \bm@next}
\makeatother


\begin{document}
%
Bold $\bm{E\left(\frac{A}{B}\right)}$
\\
Normal $E\left(\frac{A}{B}\right)$
%
\end{document}

^{[This is not a solution but a workaround]}

You say, that there is an upcoming deadline and there might be no fix available until then. Here is a workaround, which requires the amsmath package (which you most probably use). It defines \bm to use the \boldsymbol macro from amsbsy (loaded automatically by amsmath). Keep in mind that there are certain drawbacks compared to bm, but at least the symbols show up.

\documentclass{article}
\usepackage{amsmath}
\def\bm{\boldsymbol}
\begin{document}
\luatexbanner

Bold $\bm{E}$

Normal $E$
\end{document}