bidi's undefined environments in (my) LuaLaTeX system

Question

I typeset Arabic text with LuaLaTeX. I am using the following definitions and it works nicely:

\newcommand{\arabtext}[1]       % Arabic inside LTR
    {\bgroup\luatextextdir TRT\arabicfont #1\egroup}

(More expanded version here.)

A while ago, though, I've been told through a comment that "[my] definition ... is wrong" and that I might have a look at the bidi-package. Indeed I looked at it several times but never got it to work on my system. In fact, I can not even compile an example taken from the bidi-documentation itself:

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{fontspec}
\newfontfamily\Parsifont[Script=Arabic]{Arabic Typesetting}
\usepackage{bidi}
\begin{document}
\begin{RTL}
Anyone who reads Old and Middle English \LRE{Short LTR text} literary texts will be familiar with the mid-brown volumes of the EETS, with the symbol of Alfred's jewel embossed on the front cover.
\begin{LTR}
Anyone who reads Old and Middle English \RLE{Short RTL text} literary texts will be familiar with the mid-brown volumes of the EETS, with the symbol of Alfred's jewel embossed on the front cover.
\end{LTR}
\end{RTL}
\end{document}

The only result is LaTeX Error: Environment RTL undefined.

Why is that so? is bidi incompatible with LuaLaTeX?

I am asking, because I do believe that bidi could be a better solution than mine offered above (because, e.g., bidi has many other feature such as RTL footnotes etc.) and would like to try and to use it.