I created a simple BibTeX file as well as a simple LaTeX file that references said BibTeX file. When I compile document in AUCTeX using C-c C-a, the bibliography section doesn't appear and the citations are broken: according to the AUCTeX manual this command should run the LaTeX-BibTeX-LaTeX-LaTeX cycle. The file itself is fine as verified by running the same cycle manually.
%% Bibliography.bib
@book{WEN08,
Author = {Jochen Wengenroth},
Date-Added = {2017-05-08 08:16:51 +0000},
Date-Modified = {2017-05-08 08:19:24 +0000},
Publisher = {de Gruyter},
Title = {Wahrscheinlichkeitstheorie},
Year = {2008}}
%% MyDoc.tex
\documentclass[11pt]{article}
\usepackage{cite}
\begin{document}
\title{My Article}
\author{Nobody Jr.}
\date{Today}
\maketitle
Blablabla said Nobody ~\cite{WEN08}.
\bibliography{Bibliography}{}
\bibliographystyle{plain}
\end{document}
AUCTeX 11.90.0
Emacs 25.1.1
TeX Live 2016, v. 3.14159265
macOS Sierra, v. 10.12.4
C-c: the first attempt has “Default LaTeX”, the subsequent ones have “Default View”. There's no offer about doing BibTeX, soC-c C-adoesn't do it either. So it seems a bug of AUC-TeX: it is supposed to do that, but it doesn't – egreg May 8 '17 at 9:29