How do I get babel to use the same typeface for regular and bold Hebrew text?

As already mentioned using XeLaTeX and polyglossia is the only way to go. Nice fonts are available for free from the Culmus Project, the Society of Biblical Literature and SIL International. Btw., fonts from these three sources also work nicely with nikkud (vowel signs) and te'amim (cantillation signs). If I am not mistaken, the very nice Frank Ruehl font is even included in Windows.

Here is a short example which uses Culmus' David CLM:

% !TEX encoding = UTF-8 Unicode
% !TEX TS-program = xelatex
\documentclass[14pt,a4paper]{scrbook}
\usepackage{xltxtra}
\usepackage{polyglossia}
\setdefaultlanguage[calendar=hebrew,numerals=hebrew]{hebrew}
\setmainfont{David CLM} % put your font of choice right here

\begin{document}
מָתֵמָטִיקָה היא המדע העוסק במושגים כגון כמות, מבנה, מרחב ושינוי
\end{document}

Unfortunately most (if not all) editors are still a pain in the a.. when it comes to writing Hebrew. For instance writing just the word "מתמטיקה" in bold face in texmaker looks like this:

\begin{document}
\textbf{מָתֵמָטִיקָה} היא המדע העוסק במושגים כגון כמות, מבנה, מרחב ושינוי.
\end{document}

Well, to get your 'ideal' solution, you could install the Culmus Package - which changes the default Hebrew font to David, and the default bold font to David Bold - like in your example, I think.

But to answer your actual question, the place to do this would be in tex/generic/babel/lhecmr.fd (at least on my installation that's the location). Relevant snippet:

\DeclareFontFamily{LHE}{cmr}{\hyphenchar\font45}
\DeclareFontShape{LHE}{cmr}{m}{n}
      {<-> jerus10 }{}
% etc. etc.
\DeclareFontShape{LHE}{cmr}{bx}{n}
      {<-> deads10 }{}
\DeclareFontShape{LHE}{cmr}{b}{n}
      {<-> deads10 }{}

and of course there are more lines for more shapes. Unfortunately, it seems that a bold version of the Jerusalem font doesn't exist. See this listing of the fonts you can use. Someone has to actually create a bold version. If you're dead set against the dead sea (excuse the pun), try:

\hadgesh{מלל בעברית}.

to get a 'poor man's bold' of whatever font is being used.

PS - After 25 years, the babel file still says (test version: still liable to change) in the file version line...