Problem with the \mathbf command

You can simply load unicode-math

MWE:

\documentclass[10 pt]{beamer}
\usetheme{default}
\usepackage{lmodern} % load a font with all the characters
\usepackage{fontspec}
\usepackage{amsmath}%loads amsmath that should go before unicode-math
\usepackage{unicode-math}
\usepackage{cmbright}
\SetSymbolFont{largesymbols}{normal}{OMX}{iwona}{m}{n}
\usefonttheme{professionalfonts}
\defaultfontfeatures{Mapping=tex-text}  % This seems to be important for mapping glyphs properly

\begin{document}
\begin{frame}
\[
\|x\|_{\mathbf{H}}
\]
\end{frame}
\end{document} 

For sizes below 10pt the cmbright package is subsetting bold fonts (which don't exists) and uses the normal weight instead. You can change this by adding this code behind cmbright:

\usepackage{cmbright}
\fontencoding{OT1}\fontfamily{cmbr}\selectfont %to load ot1cmbr.fd
\DeclareFontShape{OT1}{cmbr}{bx}{n}{% change bx definition
<->cmbrbx10%
}{}
\normalfont % back to normalfont