Change Bibliography Title using Natbib, Polyglossia, BibTeX, and XeLaTeX

Question

I'm writing a document in Hebrew, but my references are entirely in English. Because of issues with text alignment in RTL languages, the bibliography is contained in an English block:

\addcontentsline{toc}{chapter}{ביבליוגרפיה} %Ideally this will be removed when a solution is found
\begin{english}
\bibliographystyle{apalike}
\bibliography{./bibliography}
\end{english}

Even so, because the document is in Hebrew, the title of the bibliography needs to be right-aligned and manually set to be in Hebrew. If I remove the \begin{english} block, the bibliography title is correctly formatted fits Hebrew (I assume this is the work of polyglossia), but the references themselves are badly muddled up - punctuation in particular is ruined entirely.

I imagine the solution will either be to render the bibliography without the title and add it in manually or to override whatever it is polyglossia does to change the bibliography title. I have found no way to do either.

MWE:

% Compiled with XeLaTeX
\documentclass[12pt]{report}

\usepackage[sort]{natbib}
\usepackage{polyglossia}
\usepackage{bidi}
\setdefaultlanguage{hebrew}
\setotherlanguage{english}
\addto\captionsenglish{
  \renewcommand{\bibname}{ביבליוגרפיה} % Swap bibliography title to Hebrew
}
\begin{document}
\setRL
לורם איפסום דולור סיט אמת

% Bibliography:
\clearpage %This replaces the page break at the start of the bibliography
\addcontentsline{toc}{chapter}{ביבליוגרפיה} 
\begin{english} % Insert the bibliography in English
    \bibliographystyle{apalike}
    \bibliography{./bibliography}
\end{english}
\end{document}

Answer 1

Yes, there is definitely an easier way to change the bibliography heading for natbib. You can do this, using the below code:

\renewcommand{\bibsection}{\section*{Whatever You Prefer}}

Note that the use of section* here ensures that the Bibliography section is not numbered, as previously suggested in a comment by Christoph90.

Answer 2

In the technical sense of the word, this is an answer, but it's not acceptable because there is bound to be a more elegant solution. It is at best an example of the desired effect.

\documentclass[12pt]{report}

\usepackage[sort]{natbib}
\usepackage{polyglossia}
\usepackage{bidi}
\setdefaultlanguage{hebrew}
\setotherlanguage{english}
\addto\captionsenglish{
  \renewcommand{\bibname}{} % Empty bibliography title
}
\begin{document}
\setRL
לורם איפסום דולור סיט אמת

% Bibliography:
\clearpage %This replaces the page break at the start of the bibliography
\begingroup
    \let\clearpage\relax % Omit the page break at the start of the bibliography
    \addcontentsline{toc}{chapter}{ביבליוגרפיה} % Because starred chapters don't add to the TOC
    \chapter*{ביבליוגרפיה} % Manually add the title without numbering
    \vspace{-86pt} % Empty chapters add lots of vspace which is normally useful. Manually remove it
    \begin{english} % Insert the bibliography in English
        \bibliographystyle{apalike}
        \bibliography{./bibliography}
    \end{english}
\endgroup
\end{document}