Your issue is "font-dependent".
Background
Indeed, special shapes of a font (bold, italic, slanted, small caps) are not defined relatively to a main font (its regular shape), but independently. The "bold version" of a font is defined per se (it is an independent *otf
, *.ttf
-file you can install and use, even if you don't have the main/regular version), and not as an homothetic transformation of the main font.
This is why we often refer to a font-family, that is the different shapes of a font (i.e. regular ("main font"), bold, italic, slanted, bold+italic, bold+slanted, small-caps, etc. versions). Some font-families have a lot of versions/shapes (e.g. not only bold, but also semi-bold), some others only one (there is no bold nor italic versions).
To be complete, a font-family has only shapes variations. Yet neither serif, nor sans-serif are shapes - they are characteristic of a font-family. A font-family is thus either serif, or sans-serif (or mono-spaced, etc.). Over font-families, there are thus font-harmonies, that are a selection of one serif font-family, one sans-serif font family, one mono-spaced ("typewriter") font-family, etc. that goes well the one with the other.
Answer
So the output produce depends on the font-family (thus the font-harmony) used by LaTeX
during the compilation: if the bold+{italic/slanted}
version of the sans-serif font-family is not installed on your computer (often because it doesn't exist), you cannot achieve what you want.
By default, LaTeX
uses the Computer Modern
font-harmony. Its sans-serif font-family doesn't have a bold + {italic/slanted}
shape version. So you cannot get what you want.
\documentclass{article}
\begin{document}
Some normal text.
\textsf{\textbf{Blah blah \emph{P. aeruginosa}}}
Some normal text.
\textsf{\textbf{Blah blah \textit{P. aeruginosa}}}
Some normal text.
\textsf{\textbf{Blah blah \textsl{P. aeruginosa}}}
\end{document}

However, when you load e.g. the lmodern
-package, you tell LaTeX
to use the Latin Modern
font-harmony. Since its sans-serif font-family has a bold+italic
and a bold+slanted
version, it can produce the output you want.
\documentclass{article}
\usepackage{lmodern}
\begin{document}
Some normal text.
\textsf{\textbf{Blah blah \emph{P. aeruginosa}}}
Some normal text.
\textsf{\textbf{Blah blah \textit{P. aeruginosa}}}
Some normal text.
\textsf{\textbf{Blah blah \textsl{P. aeruginosa}}}
\end{document}

\usepackage[T1]{fontenc}
.\documentclass{...}
and ending with\end{document}
.