I hesitate to post an "It's-working-for-me" reply as an "answer", but it might provoke a refinement of OP's issue, if nothing else.
Here is something like a "MWE", using TeXstudio 2.10.8 on a Mac (early 2015) with TL 2015 installed:
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[12pt]{article}
\usepackage{fontspec,xltxtra,xunicode}
\defaultfontfeatures{Mapping=tex-text}
\setmainfont{TeX Gyre Pagella}
\newfontfamily{\Hb}{SBL Hebrew}
\usepackage{bidi}
\title{Very Trying}
\author{David}
%\date{}
\begin{document}
\maketitle
For some time now I have thought about trying to get, {\RL{\Hb מי יודע}}, RTL mixed in, for example, and distinct RTL in my LTR text:\\
\begin{RTL}
{\Hb מי כהחכם ומי יודע פשׁר דבר}\\
\end{RTL}
This is typeset by \textsf{bidi} package, version \bidiversion, \bididate.
\end{document}
A search of the PDF (using Preview) works exactly as expected:

FWIW. (The Hebrew font referenced is SBL Hebrew.)