Angstrom circle not centred

The left-offset of the ångström symbol is caused by tgbonum. You can fix this by also loading \usepackage[T1]{fontenc} after tgbonum.

I also suggest that you use siunitx's provided macro (instead of only using the package to obtain the unit), \SI, to properly typeset values with units:

$\approx \SI{3.5}{\angstrom}$

With the OT1 encoding, \r{A} is a predefined combination that doesn't use the ring accent, but uses a more complex setup, because the ring should be attached to the A. This setup fails with TeX Gyre Bonum, but it can be fixed.

I also suggest to scale down the font, because it has a rather large x-height; alternatively, you could increase the leading with \linespread{1.1} or similar.

You can get numbers with \SI in the text font by using mode=text.

\documentclass{article}
\usepackage[scale=0.94]{tgbonum}
\usepackage[mode=text]{siunitx}

\makeatletter
\DeclareTextCompositeCommand{\r}{OT1}{A}{%
  \leavevmode\vbox{%
    \offinterlineskip
    \ialign{\hfil##\hfil\cr\char23\cr\noalign{\kern-1.15ex}A\cr}%
  }%
}
\makeatother

\begin{document}

\r{A}ngstrom or \AA ngstrom \r{A}\r{U} \r{a}\r{u}

Additionally, it is accompanied by a drastic change in
end-to-end distance of~\SI{3.5}{\angstrom} as well as polarity
(3~Debye for \emph{cis} versus 0~Debye for \emph{trans}).

\end{document}

Note that using $word$ is not the way to get italics.