cmbright not allowing bold and italic

Using the lmodern and sfmath package should help.

\documentclass[a4paper,12pt]{article}
\usepackage{lmodern}
\usepackage{sfmath}

\begin{document}
\sffamily
cmbright won't allow me to \textbf{bold} and
\textit{italicise} my text
\textbf{\textit{at the same time}},
no matter \textit{\textbf{how I nest them.}}

$2a-3B$
\end{document}

The choice of sans serif families with a full range of styles is rather limited, you may get more choice if you switch to xetex or luatex and use system fonts.

This is Arial with lualatex for example

\documentclass[a4paper,12pt]{article}
\usepackage{fontspec}
\setmainfont{Arial}
\begin{document} 
cmbright won't allow me to \textbf{bold} and \textit{italicise} my text \textbf{\textit{at the same time}}, no matter \textit{\textbf{how I nest them.}} 
\end{document}